×

From Leibniz algebras to Lie 2-algebras. (English) Zbl 1378.17007

The authors construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization.

MSC:

17A32 Leibniz algebras
17B55 Homological methods in Lie (super)algebras
Full Text: DOI

References:

[1] Baez, J., Crans, A.S.: Higher-Dimensional algebra VI: Lie 2-Algebras. Theory and Appl. Categ. 12, 492-528 (2004) · Zbl 1057.17011
[2] Kosmann-Schwarzbach, Y.: Courant algebroids. A short history. SIGMA Symmetry Integrability Geom. Methods Appl. 9, 8 (2013). Paper 014 · Zbl 1268.01019
[3] Liu, Z.-J., Weinstein, A., Xu, P.: Manin triples for Lie bialgebroids. J. Diff. Geom. 45, 547-574 (1997) · Zbl 0885.58030
[4] Loday, J.-L.: Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign. Math. 39(2), 269-293 (1993) · Zbl 0806.55009
[5] Loday, J.-L., Pirashvili, T.: Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 296, 139-158 (1993) · Zbl 0821.17022 · doi:10.1007/BF01445099
[6] Roytenberg, D.: Courant algebroids, derived brackets and even symplectic supermanifolds, PhD thesis, UC Berkeley, 1999. arXiv:math.DG/9910078 · Zbl 0885.58030
[7] Roytenberg, D., Weinstein, A.: Courant algebroids and strongly homotopy Lie algebras. Lett. Math. Phys. 46(1), 81-93 (1998) · Zbl 0946.17006 · doi:10.1023/A:1007452512084
[8] Schlessinger, M., Stasheff, J.: The Lie algebra structure of tangent cohomology and deformation theory. J. Pure Appl. Alg. 38, 313-322 (1985) · Zbl 0576.17008 · doi:10.1016/0022-4049(85)90019-2
[9] Sheng, Y., Zhu, C.: Semidirect products of representations up to homotopy. Pacific J. Math. 249(1), 211-236 (2011) · Zbl 1267.17019 · doi:10.2140/pjm.2011.249.211
[10] Weinstein, A.: Omni-Lie algebras, Microlocal analysis of the Schrodinger equation and related topics (Japanese) (Kyoto, 1999). Sūrikaisekikenkyūsho Kōkyūroku No. 1176, pp. 95-102 (2000) · Zbl 1058.58503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.