Local and Linear 2-local Automorphisms of Heisenberg Lie (Super)algebras

Abstract

In this paper, we give the forms of local and linear 2-local automorphisms of Heisenberg Lie algebra and Heisenberg Lie superalgebra in matrix version.

Keywords

Automorphism / local automorphism / Heisenberg Lie (super)algebra

References

[1] Ayupov S, Kudaybergenov K. 2-Local automorphisms on finite-dimensional Lie algebras. Linear Algebra Appl., 2016, 507: 121-131.

[2] Bai W., Liu W., Cohomology of Heisenberg Lie superalgebras. J. Math. Phys., 2017, 58(2): Paper No. 021701, 14 pp.

[3] Corwin L, Greenleaf FP. Representations of Nilpotent Lie Groups and Their Applications, Part I, 1990, Cambridge: Cambridge University Press.

[4] Corwin L, Ne’eman Y, Sternberg S. Graded Lie algebras in mathematics and physics. Rev. Modern Phys., 1975, 47: 573-603.

[5] Hegazi AS. Representations of Heisenberg Lie super algebras. Indian J. Pure Appl. Math., 1990, 21(6): 557-566.

[6] Hole A. Representations of the Heisenberg group of dimension 2n + 1 on eigenspaces. Math. Scand., 1975, 37(1): 129-141.

[7] Jiang C, Meng D, Zhang S. Some complete Lie algebras. J. Algebra, 1996, 186(3): 807-817.

[8] Liu L, Tang L. The automorphism groups of Heisenberg Lie (super)algebras. J. Math. (PRC), 2018, 38(3): 502-510 (in Chinese)

[9] Liu W, Chen M. The minimal dimensions of faithful representations for Heisenberg Lie superalgebras. J. Geom. Phys., 2015, 89: 17-23.

[10] Wang L, Meng D. Some complete Lie superalgebras. Linear Algebra Appl., 2003, 369: 339-349.

[11] Yndurán FJ. The Heisenberg algebra and contractions of the rotation algebra. Nuovo Cimento A (10), 1967, 50: 308-312.

[12] Zhang H, Shao W, Lu C. The automorphism group of Heisenberg Lie algebra. J. Capital Normal Univ. (Nat. Sci. Ed.), 2007, 28: 1-7 (in Chinese)

[13] Zhou J, Chen L. Derivation algebra of the Heisenberg superalgebra. J. Jilin Univ. (Sci. Ed.), 2011, 49(3): 419-423. (in Chinese)

[14] Sköldberg E. The homology of Heisenberg Lie algebras over fields of characteristic two. Math. Proc. R. Ir. Acad., 2005, 150A(2): 47-49.