Fetching the paper…
Reading the bibliography…
We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras.
Cartan, E., “Sur certaines formes riemanniennes remarquables des géométries à groupe fondamental simple”, Ann. Sci. Ecole Norm. Sup
1927
Earlier work this paper cites.
Hilbert, D., and Cohn-Vossen, S., Geometry and the Imagination
1952
Earlier work this paper cites.
Dynkin, E.B., “Semisimple subalgebras of semisimple Lie algebras”, Trans. Amer. Math. Soc
1957
Earlier work this paper cites.
Satake, I., “On Representations and Compactifications of Symmetric Riemannian Spaces”, Ann. Math. (2)
1960
Earlier work this paper cites.
Araki, S., “On root systems and an infinitesimal classification of irreducible symmetric spaces”, Osaka J. Math
1962
Earlier work this paper cites.
Tits, J., “Classification of algebraic semisimple groups”, Proc. Symp. Pure Math
1966
Earlier work this paper cites.
DeWitt, B.S., “Quantum Theory of Gravity. I. The Canonical Theory”, Phys. Rev
1967
Earlier work this paper cites.
Loos, O., Symmetric Spaces, 2 vols
1969
Earlier work this paper cites.
Margulis, G.A., “Applications of ergodic theory to the investigation of manifolds of negative curvature”, Funct. Anal. Appl
1969
Earlier work this paper cites.
Misner, C.W., “Mixmaster Universe”, Phys. Rev. Lett
1969
Earlier work this paper cites.
Belinskii, V.A., Khalatnikov, I.M., and Lifshitz, E.M., “Oscillatory Approach To A Singular Point In The Relativistic Cosmology”, Adv. Phys
1970
Earlier work this paper cites.
Lifshitz, E.M., Lifshitz, I.M., and Khalatnikov, I.M., Sov. Phys. JETP
1971
Earlier work this paper cites.
Chitre, D.M., Investigations of Vanishing of a Horizon for Bianchy Type X (the Mixmaster)
1972
Earlier work this paper cites.
Belinskii, V.A., and Khalatnikov, I.M., “Effect of scalar and vector fields on the nature of the cosmological singularity”, Sov. Phys. JETP
1973
Earlier work this paper cites.
Hawking, S.W., and Ellis, G.F.R., The Large Scale Structure of Space-Time
1973
Earlier work this paper cites.
Deser, S., and Teitelboim, C., “Duality Transformations of Abelian and Nonabelian Gauge Fields”, Phys. Rev. D
1976
Earlier work this paper cites.
Cremmer, E., and Julia, B., “The N = 8 N=8 Supergravity Theory. 1. The Lagrangian”, Phys. Lett. B
1978
Earlier work this paper cites.
Cremmer, E., Julia, B., and Scherk, J., “Supergravity theory in 11 dimensions”, Phys. Lett. B
1978
Earlier work this paper cites.
Cremmer, E., and Julia, B., “The S O ( 8 ) SO(8) Supergravity”, Nucl. Phys. B
1979
Earlier work this paper cites.
Aurilia, A., Nicolai, H., and Townsend, P.K., “Hidden Constants: The Theta Parameter of QCD and the Cosmological Constant of N = 8 N=8 Supergravity”, Nucl. Phys. B
1980
Earlier work this paper cites.
Julia, B., “Group disintegrations”, in Hawking, S.W., and Roček, M., eds., Superspace and Supergravity
1981
Earlier work this paper cites.
Bergshoeff, E., de Roo, M., de Wit, B., and van Nieuwenhuizen, P., “Ten-dimensional Maxwell-Einstein supergravity, its currents, and the issue of its auxiliary fields”, Nucl. Phys. B
1982
Earlier work this paper cites.
Helminck, A.G., “Classification of real semisimple Lie algebras”, in Koornwinder, T.H., ed., The structure of real semisimple Lie groups
1982
Earlier work this paper cites.
Chapline, G.F., and Manton, N.S., “Unification of Yang-Mills Theory and Supergravity in Ten- Dimensions”, Phys. Lett. B
1983
Earlier work this paper cites.
Chernoff, D.F., and Barrow, J.D., “Chaos in the Mixmaster Universe”, Phys. Rev. Lett
1983
Earlier work this paper cites.
Feingold, A.J., and Frenkel, I.B., “A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2”, Math. Ann
1983
Earlier work this paper cites.
Marcus, N., and Schwarz, J.H., “Three-Dimensional Supergravity Theories”, Nucl. Phys. B
1983
Earlier work this paper cites.
Henneaux, M., and Teitelboim, C., “The cosmological constant as a canonical variable”, Phys. Lett. B
1984
Earlier work this paper cites.
Kac, V.G., “Laplace operators of infinite-dimensional Lie algebras and theta functions”, Proc. Natl. Acad. Sci. USA
1984
Earlier work this paper cites.
Page, W., and Dorwart, H.L., “Numerical Patterns and geometric Configurations”, Math. Mag
1984
Earlier work this paper cites.
Zimmer, R.J., Ergodic Theory and Semisimple Groups
1984
Earlier work this paper cites.
Curtright, T., “Generalized gauge fields”, Phys. Lett. B
1985
Earlier work this paper cites.
Demaret, J., Hanquin, J.L., Henneaux, M., and Spindel, P., “Cosmological models in eleven-dimensional supergravity”, Nucl. Phys. B
1985
Earlier work this paper cites.
Demaret, J., Henneaux, M., and Spindel, P., “No Oscillatory Behavior in vacuum Kaluza-Klein cosmologies”, Phys. Lett. B
1985
Earlier work this paper cites.
Gross, D.J., Harvey, J.A., Martinec, E.J., and Rohm, R., “The Heterotic String”, Phys. Rev. Lett
1985
Earlier work this paper cites.
Khalatnikov, I.M., Lifshitz, E.M., Khanin, K.M., Shchur, L.N., and Sinai, Y.G., “On The Stochasticity In Relativistic Cosmology”, J. Stat. Phys
1985
Earlier work this paper cites.
Demaret, J., Hanquin, J.L., Henneaux, M., Spindel, Ph., and Taormina, A., “The fate of the mixmaster behavior in vacuum inhomogeneous Kaluza-Klein cosmological models”, Phys. Lett. B
1986
Earlier work this paper cites.
Elskens, Y., and Henneaux, M., “Ergodic theory of the mixmaster model in higher space-time dimensions”, Nucl. Phys. B
1987
Earlier work this paper cites.
Nicolai, H., “ D = 11 D=11 Supergravity With Local S O ( 16 ) SO(16) Invariance”, Phys. Lett. B
1987
Earlier work this paper cites.
Nicolai, H., “The integrability of N = 16 N=16 supergravity”, Phys. Lett. B
1987
Earlier work this paper cites.
Breitenlohner, P., Maison, D., and Gibbons, G.W., “Four-dimensional black holes from Kaluza-Klein theories”, Commun. Math. Phys
1988
Earlier work this paper cites.
Demaret, J., De Rop, Y., and Henneaux, M., “Chaos in Nondiagonal Spatially Homogeneous Cosmological Models in Space-time Dimensions ≤ 10 \leq 10 ”, Phys. Lett. B
1988
Earlier work this paper cites.
Henneaux, M., and Teitelboim, C., “Dynamics of chiral (selfdual) p p -forms”, Phys. Lett. B
1988
Earlier work this paper cites.
Saçlioğlu, C., “Dynkin diagrams for hyperbolic Kac-Moody algebras”, J. Phys. A
1989
Earlier work this paper cites.
Humphreys, J.E., Reflection Groups and Coxeter Groups
1990
Earlier work this paper cites.
Kac, V.G., Infinite dimensional Lie algebras
1990
Earlier work this paper cites.
Fuchs, J., Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory
1992
Earlier work this paper cites.
Ruuska, V., “On purely hyperbolic Kac-Moody algebras”, in Mickelsson, J., and Pekonen, O., eds., Topological and Geometrical Methods in Field Theory
1992
Earlier work this paper cites.
Kirillov, A.A., “The Nature of the Spatial Distribution of Metric Inhomogeneities in the General Solution of the Einstein Equations near a Cosmological Singularity”, J. Exp. Theor. Phys
1993
Earlier work this paper cites.
Spindel, Ph., and Zinque, M., “Asymptotic behavior of the Bianchi IX cosmological models in the R**2 theory of gravity”, Int. J. Mod. Phys. D
1993
Earlier work this paper cites.
Vinberg, E.B., ed., Geometry II: Spaces of Constant Curvature
1993
Earlier work this paper cites.
Ivashchuk, V.D., Kirillov, A.A., and Melnikov, V.N., “Stochastic behavior of multidimensional cosmological models near a singularity”, Russ. Phys. J
1994
Earlier work this paper cites.
Ivashchuk, V.D., Melnikov, V.N., and Kirillov, A.A., “Stochastic properties of multidimensional cosmological models near a singular point”, JETP Lett
1994
Earlier work this paper cites.
Ratcliffe, J.G., Foundations of Hyperbolic Manifolds
1994
Earlier work this paper cites.
Apostol, T.M., Modular Functions and Dirichlet Series in Number Theory
1997
Earlier work this paper cites.
Fuchs, J., and Schweigert, C., Symmetries, Lie Algebras and Representations: A graduate course for physicists
1997
Earlier work this paper cites.
Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces
2001
Cited alongside, same era.
Knapp, A.W., Lie Groups Beyond an Introduction
2002
Cited alongside, same era.
Kleinschmidt, A., Indefinite Kac-Moody Algebras in String Theory
2004
Cited alongside, same era.
Bahls, P., The Isomorphism Problem in Coxeter Groups
2005
Cited alongside, same era.
Ben Messaoud, H., “Almost split real forms for hyperbolic Kac-Moody Lie algebras”, J. Phys. A
2006
Cited alongside, same era.
Alekseev, A., and Monnier, S., “Quantization of Wilson loops in Wess-Zumino-Witten models”, J. High Energy Phys
2007
Cited alongside, same era.
Forte, L.A., and Sciarrino, A., “Standard and non-standard extensions of Lie algebras”, J. Math. Phys
2007
Closest in time.
Fré, P., et al., “Cosmological backgrounds of superstring theory and solvable algebras: Oxidation and branes”, Nucl. Phys. B
2007
Closest in time.
Fré, P., Gargiulo, F., and Rulik, K., “Cosmic billiards with painted walls in non-maximal supergravities: A worked out example”, Nucl. Phys. B
2007
Closest in time.
Fré, P., Gargiulo, F., Rulik, K., and Trigiante, M., “The general pattern of Kac-Moody extensions in supergravity and the issue of cosmic billiards”, Nucl. Phys. B
2007
Closest in time.
Fré, P., Rulik, K., and Trigiante, M., “Exact solutions for Bianchi type cosmological metrics, Weyl orbits of E 8 ( 8 ) E_{8(8)} subalgebras and p p -branes”, Nucl. Phys. B
2007
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Andersson, L., “On the relation between mathematical and numerical relativity”, Class. Quantum Grav
2007
Cited alongside, same era.
Andersson, L., and Rendall, A.D., “Quiescent cosmological singularities”, Commun. Math. Phys
2007
Cited alongside, same era.
Argurio, R., Englert, F., and Houart, L., “Intersection rules for p-branes”, Phys. Lett. B
2007
Cited alongside, same era.
Baez, J.C., “The Octonions”, (2001). URL (cited on 19 October 2007): http://arXiv.org/abs/math.ra/0105155
2007
Cited alongside, same era.
Bagnoud, M., and Carlevaro, L., “Hidden Borcherds symmetries in Z n Z_{n} orbifolds of M-theory and magnetized D D -branes in type 0’ orientifolds”, J. High Energy Phys
2007
Cited alongside, same era.
2007
Cited alongside, same era.
2007
Closest in time.
Gaberdiel, M.R.and Olive, D.I., and West, P.C., “A class of Lorentzian Kac-Moody algebras”, Nucl. Phys. B
2007
Closest in time.
Garfinkle, D., “Numerical simulations of generic singuarities”, Phys. Rev. Lett
2007
Closest in time.
Green, M.B., and Vanhove, P., “Duality and higher derivative terms in M theory”, J. High Energy Phys
2007
Closest in time.
Gutperle, M., and Strominger, A., “Spacelike branes”, J. High Energy Phys
2007
Closest in time.
Heinzle, J.M., Uggla, C., and Rohr, N., “The cosmological billiard attractor”, (2007). URL (cited on 19 October 2007): http://arXiv.org/abs/gr-qc/0702141
2007
Closest in time.
Henneaux, M., and Julia, B., “Hyperbolic billiards of pure D = 4 D=4 supergravities”, J. High Energy Phys
2007
Closest in time.
Henneaux, M., Leston, Mauricio, Persson, D., and Spindel, Ph., “Geometric configurations, regular subalgebras of E 10 E_{10} and M-theory cosmology”, J. High Energy Phys
2007
Closest in time.
Henneaux, M., Leston, Mauricio, Persson, D., and Spindel, Ph., “A Special Class of Rank 10 and 11 Coxeter Groups”, J. Math. Phys
2007
Closest in time.
Henneaux, M., and Teitelboim, C., “Duality in linearized gravity”, Phys. Rev. D
2007
Closest in time.
Henry-Labordere, P., Julia, B., and Paulot, L., “Borcherds symmetries in M-theory”, J. High Energy Phys
2007
Closest in time.
Henry-Labordere, P., Julia, B., and Paulot, L., “Real Borcherds superalgebras and M-theory”, J. High Energy Phys
2007
Closest in time.
Henry-Labordere, P., Julia, B., and Paulot, L., “Symmetries in M-theory: Monsters, Inc”, Cargese 2002, conference paper, (2003). Related online version (cited on 19 October 2007): http://arXiv.org/abs/hep-th/0303178
2007
Closest in time.
Hillmann, C., and Kleinschmidt, A., “Pure type I supergravity and D E 10 DE_{10} ”, Gen. Relativ. Gravit
2007
Closest in time.
Isenberg, J., and Moncrief, V., “Asymptotic Behavior of Polarized and Half-Polarized U ( 1 ) U(1) symmetric Vacuum Spacetimes”, Class. Quantum Grav
2007
Closest in time.
Ivashchuk, V.D., and Melnikov, V.N., “Billiard representation for multidimensional cosmology with multicomponent perfect fluid near the singularity”, Class. Quantum Grav
2007
Closest in time.
Ivashchuk, V.D., and Melnikov, V.N., “Billiard representation for multidimensional cosmology with intersecting p-branes near the singularity”, J. Math. Phys
2007
Closest in time.
Julia, B., Levie, J., and Ray, S., “Gravitational duality near de Sitter space”, J. High Energy Phys
2007
Closest in time.
Keurentjes, A., “The group theory of oxidation”, Nucl. Phys. B
2007
Closest in time.
Keurentjes, A., “The group theory of oxidation. II: Cosets of non-split groups”, Nucl. Phys. B
2007
Closest in time.
Keurentjes, A., “Poincare duality and 𝒢 + + + \mathcal{G}^{+++} algebras”, (2005). URL (cited on 19 October 2007): http://arXiv.org/abs/hep-th/0510212
2007
Closest in time.
Kirillov, A.A., and Melnikov, V.N., “Dynamics of inhomogeneities of metric in the vicinity of a singularity in multidimensional cosmology”, Phys. Rev. D
2007
Closest in time.
Kleinschmidt, A., and Nicolai, H., “ E 10 E_{10} and S O ( 9 , 9 ) SO(9,9) invariant supergravity”, J. High Energy Phys
2007
Closest in time.
Kleinschmidt, A., and Nicolai, H., “IIB supergravity and E 10 E_{10} ”, Phys. Lett. B
2007
Closest in time.
Kleinschmidt, A., and Nicolai, H., “ E 10 E_{10} cosmology”, J. High Energy Phys
2007
Closest in time.
Kleinschmidt, A., Nicolai, H., and Palmkvist, J., “ K ( E 9 ) K(E_{9}) from K ( E 10 ) K(E_{10}) ”, J. High Energy Phys
2007
Closest in time.
Lambert, N., and West, P., “Duality groups, automorphic forms and higher derivative corrections”, Phys. Rev. D
2007
Closest in time.
Lambert, N., and West, P.C., “Enhanced coset symmetries and higher derivative corrections”, Phys. Rev. D
2007
Closest in time.
2007
Closest in time.
Misner, C.W., “The Mixmaster cosmological metrics”, (1994). URL (cited on 19 October 2007): http://arXiv.org/abs/gr-qc/9405068
2007
Closest in time.
Nicolai, H., and Fischbacher, T., “Low level representations for E 10 E_{10} and E 11 E_{11} ”, (2003). URL (cited on 19 October 2007): http://arXiv.org/abs/hep-th/0301017
2007
Closest in time.
Obers, N.A., and Pioline, B., “U-duality and M-theory”, Phys. Rep
2007
Closest in time.
Ohta, N., “Accelerating cosmologies from S-branes”, Phys. Rev. Lett
2007
Closest in time.
Ohta, N., “Intersection rules for S-branes”, Phys. Lett. B
2007
Closest in time.
Rendall, A.D., “The Nature of Spacetime Singularities”, in Ashtekar, A., ed., 100 Years of Relativity. Space-Time Structure: Einstein and Beyond
2007
Closest in time.
2007
Closest in time.
Riccioni, F., and West, P., “Dual fields and E 11 E_{11} ”, Phys. Lett. B
2007
Closest in time.
2007
Closest in time.
Ringstrom, H., “The Bianchi IX attractor”, Ann. Henri Poincare
2007
Closest in time.
Russo, J.G., and Tseytlin, A.A., “One-loop four-graviton amplitude in eleven-dimensional supergravity”, Nucl. Phys. B
2007
Closest in time.
Schnakenburg, I., and West, P.C., “Kac-Moody symmetries of IIB supergravity”, Phys. Lett. B
2007
Closest in time.
Schnakenburg, I., and West, P.C., “Massive IIA supergravity as a non-linear realisation”, Phys. Lett. B
2007
Closest in time.
Schnakenburg, I., and West, P.C., “Kac-Moody symmetries of ten-dimensional non-maximal supergravity theories”, J. High Energy Phys
2007
Closest in time.
Schwarz, J.H., and Sen, A., “Duality symmetric actions”, Nucl. Phys. B
2007
Closest in time.
2007
Closest in time.
Uggla, C., van Elst, H., Wainwright, J., and Ellis, G.F.R., “The past attractor in inhomogeneous cosmology”, Phys. Rev. D
2007
Closest in time.
Wesley, D.H., “Kac-Moody algebras and controlled chaos”, Class. Quantum Grav
2007
Closest in time.
Wesley, D.H., Steinhardt, P.J., and Turok, N., “Controlling chaos through compactification in cosmological models with a collapsing phase”, Phys. Rev. D
2007
Closest in time.
West, P., “The IIA, IIB and eleven dimensional theories and their common E 11 E_{11} origin”, Nucl. Phys. B
2007
Closest in time.
West, P., “ E 11 E_{11} and Higher Spin Theories”, (2007). URL (cited on 19 October 2007): http://arXiv.org/abs/hep-th/0701026
2007
Closest in time.
West, P.C., “ E 11 E_{11} and M theory”, Class. Quantum Grav
2007
Closest in time.