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We study the semidirect product of a Lie algebra with a representation up to homotopy and provide various examples coming from Courant algebroids, string Lie 2-algebras, and omni-Lie algebroids.
Omni-Lie algebroids, arXiv:0710.1923. to appear in J. Geom. Phys
Z. Chen and Z.-J. Liu · 1923
Earlier work this paper cites.
Poisson Lie groups, dressing transformations, and Bruhat decompositions
J.-H. Lu and A. Weinstein · 1990
Earlier work this paper cites.
Differential graded Lie algebras, quasi-Hopf algebras and higher homotopy algebras
J. Stasheff · 1992
Earlier work this paper cites.
Loop spaces, characteristic classes and geometric quantization
J.-L. Brylinski · 1993
Earlier work this paper cites.
Manin triples for Lie bialgebroids
Z.-J. Liu, A. Weinstein, and P. Xu · 1997
Cited alongside, same era.
Courant algebroids and strongly homotopy Lie algebras
D. Roytenberg and A. Weinstein · 1998
Cited alongside, same era.
On the structure of graded symplectic supermanifolds and Courant algebroids
D. Roytenberg · 2002
Cited alongside, same era.
Higher-dimensional algebra. VI. Lie 2-algebras
J. C. Baez and A. S. Crans · 2004
Cited alongside, same era.
Representations up to homotopy of Lie algebroids, arxiv:math.DG/0403269
C. Abad and M. Crainic
Cited in the paper.
Categorified Symplectic Geometry and the String Lie 2-Algebra, arXiv:0901.4721
J. C. Baez and C. L. Rogers
Cited in the paper.
Extensions of Lie brackets, arXiv:0810.1462, to appear in J. Geom. Phys
O. Brahic
Cited in the paper.
Dirac structures of omni-Lie algebroids, arXiv:0802.3819
Z. Chen, Z.-J. Liu, and Y.-H. Sheng
Cited in the paper.
E E -Courant algebroids, arXiv:0802.3819
Z. Chen, Z.-J. Liu, and Y.-H. Sheng
Cited in the paper.
Lie theory for nilpotent L-infinity algebras, arxiv:math.AT/0404003
E. Getzler
Cited in the paper.
A Finite Dimensional String 2-Group, in preparation
C. Schommer-Pries
Cited in the paper.
Integration of central extensions of Lie 2-algebras, in preparation
C. Schommer-Pries, C. Wockel, and C. Zhu
Cited in the paper.
Higher-dimensional algebra. V. 2-groups
J. C. Baez and A. D. Lauda · 2004
Later among the works it cites.
Representation up to homotopy and cohomology of classifying spaces
C. Abad · 2008
Later among the works it cites.
Stacky Lie groups
C. Blohmann · 2008
Later among the works it cites.
Integrating L ∞ L_{\infty} -algebras
A. Henriques · 2008
Later among the works it cites.
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