|
|
|
Omni-Lie superalgebras and Lie 2-superalgebras |
Tao ZHANG,Zhangju LIU( ) |
| Department of Mathematics and LMAM, Peking University, Beijing 100871, China |
|
|
|
|
Abstract We introduce the notion of omni-Lie superalgebras as a super version of an omni-Lie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2-superalgebras. We prove that there is a one-to-one correspondence between Dirac structures of the omni-Lie superalgebra and Lie superalgebra structures on a subspace of a super vector space.
|
| Keywords
Lie 2-superalgebra
Leibniz superalgebra
Dirac structure
|
|
Corresponding Author(s):
Zhangju LIU
|
|
Issue Date: 26 August 2014
|
|
| 1 |
Albeverio S, Ayupov S A, Omirov B A. On nilpotent and simple Leibniz algebras. Comm Algebra, 2005, 33: 159-172
doi: 10.1081/AGB-200040932
|
| 2 |
Baez J, Crans A S. Higher-dimensional algebra VI: Lie 2-Algebras. Theory Appl Categ, 2004, 12: 492-528
|
| 3 |
Barreiro E, Benayadi S. Quadratic symplectic Lie superalgebras and Lie bisuperalgebras. J Algebra, 2009, 321: 582-608
doi: 10.1016/j.jalgebra.2008.09.026
|
| 4 |
Bursztyn H, Cavalcanti G, Gualteri M. Reduction of Courant algebroids and generalized complex structures. Adv Math, 2007, 211: 726-765
doi: 10.1016/j.aim.2006.09.008
|
| 5 |
Chen Z, Liu Z J. Omni-Lie algebroids. J Geom Phys, 2010, 60: 799-808
doi: 10.1016/j.geomphys.2010.01.007
|
| 6 |
Chen Z, Liu Z J, Sheng Y. Dirac structures of omni-Lie algebroids. Int J Math, 2011, 22: 1163-1185
doi: 10.1142/S0129167X11007215
|
| 7 |
Huerta J. Division Algebras, Supersymmetry and Higher Gauge Theory. Ph D Thesis. University of California, 2011, arXiv: 1106.3385
|
| 8 |
Kac V G. Lie superalgebras. Adv Math, 1977, 26: 8-96
doi: 10.1016/0001-8708(77)90017-2
|
| 9 |
Kinyon K, Weinstein A. Leibniz algebras, Courant algebroids, and multiplications on reductive homogeneous spaces. Amer J Math, 2001, 123: 525-550
doi: 10.1353/ajm.2001.0017
|
| 10 |
Lada T, Stasheff J. Introduction to sh Lie algebras for physicists. Int J Theor Phys, 1993, 32: 1087-1103
doi: 10.1007/BF00671791
|
| 11 |
Liu Z J. Some remarks on Dirac structures and Poisson reductions. In: Poisson Geometry (Warsaw, 1998). Banach Center Publ, Vol 51. Warsaw: Polish Acad Sci, 2000, 165-173
|
| 12 |
Loday J L. Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Enseign Math, 1993, 39: 269-293
|
| 13 |
Roytenberg D, Weinstein A. Courant algebroids and strongly homotopy Lie algebras. Lett Math Phys, 1998, 46: 81-93
doi: 10.1023/A:1007452512084
|
| 14 |
Scheunert M. The Theory of Lie Superalgebras. Lecture Note in Mathematics 716. Berlin: Springer, 1979
|
| 15 |
Sheng Y, Liu Z J, Zhu C C. Omni-Lie 2-algebras and their Dirac structures. J Geom Phys, 2011, 61: 560-575
doi: 10.1016/j.geomphys.2010.11.005
|
| 16 |
Uchino K. Courant brackets on noncommutative algebras and omni-Lie algebras. Tokyo J Math, 2007, 30: 239-255
doi: 10.3836/tjm/1184963659
|
| 17 |
Weinstein A. Omni-Lie Algebras. RIMS K?ky?roku Bessatsu, 2000, 1176: <?Pub Caret1?>95-102
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
