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S. M. Kasymov, “On a theory of n n -Lie algebras,” Algebra i Logika
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Similar

J. M. Figueroa-O’Farrill and S. Stanciu, “Nonsemisimple Sugawara constructions,” Phys. Lett
1994
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J. M. Figueroa-O’Farrill and S. Stanciu, “On the structure of symmetric selfdual Lie algebras,” J. Math. Phys
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1997
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J. Bagger and N. Lambert, “Gauge symmetry and supersymmetry of multiple M2-branes,” Phys. Rev
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2008
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J. Bagger and N. Lambert, “Comments on multiple M2-branes,” JHEP
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2008
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M. A. Bandres, A. E. Lipstein, and J. H. Schwarz, “N = 8 superconformal Chern–Simons theories,” JHEP
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2008

Metric Lie 3-algebras in Bagger-Lambert theory

de Medeiros, Paul, Figueroa-O'Farrill, José, Méndez-Escobar, Elena

Understand

We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations.

We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras.
We classify metric Lie 3-algebras of signature (2,p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product.
We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2,p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.

Built on

V. Filippov, “ n n -Lie algebras,” Sibirsk. Mat. Zh
1985
Earlier work this paper cites.
A. Medina and P. Revoy, “Algèbres de Lie et produit scalaire invariant,” Ann. scient. Éc. Norm. Sup
1985
Earlier work this paper cites.
A. Medina, “Groupes de Lie munis de métriques bi-invariantes,” Tōhoku Math. J. (2)
1985
Earlier work this paper cites.
S. M. Kasymov, “On a theory of n n -Lie algebras,” Algebra i Logika
1987
Earlier work this paper cites.
S. Cecotti and A. Sen, “Coulomb branch of the lorentzian three-algebra theory,” arXiv:0806.1990 [hep-th]
Original
1990
Earlier work this paper cites.
PhD thesis, Siegen, 1993
W. X. Ling, On the structure of n n -Lie algebras · 1993
Earlier work this paper cites.
C. Nappi and E. Witten, “A WZW model based on a non-semi-simple group,” Phys. Rev. Lett
1993
Earlier work this paper cites.

Similar

J. M. Figueroa-O’Farrill and S. Stanciu, “Nonsemisimple Sugawara constructions,” Phys. Lett
1994
Cited alongside, same era.
J. M. Figueroa-O’Farrill and S. Stanciu, “On the structure of symmetric selfdual Lie algebras,” J. Math. Phys
1996
Cited alongside, same era.
H. Fuji, S. Terashima, and M. Yamazaki, “A new N = 4 N=4 membrane action via orbifold,” arXiv:0805.1997 [hep-th]
Original
1997
Cited alongside, same era.
J. H. Schwarz, “Superconformal Chern-Simons theories,” JHEP
2004
Cited alongside, same era.
J. M. Figueroa-O’Farrill and G. Papadopoulos, “Plücker-type relations for orthogonal planes,” J. Geom. Phys
2004
Cited alongside, same era.
I. Kath and M. Olbrich, “Metric Lie algebras with maximal isotropic centre,” Math. Z