Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 1: 203 - 216

DOI: https://doi.org/10.1007/s11464-012-0185-6

RESEARCH ARTICLE

Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras

  • Jixia YUAN 1 ,
  • Wende LIU , 2
Expand
  • 1. School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China
  • 2. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China

Received date: 01 Jan 2010

Accepted date: 04 Jan 2012

Published date: 01 Feb 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

The principal filtration of the infinite-dimensional odd contact Lie superalgebra over a field of characteristic p>2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd contact superalgebras are classified up to isomorphisms.

Key words： Lie superalgebra; filtration; automorphism; classification

Cite this article

Jixia YUAN , Wende LIU . Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras[J]. Frontiers of Mathematics in China, 2013 , 8(1) : 203 -216 . DOI: 10.1007/s11464-012-0185-6

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Kac V G. Classification of infinite-dimensional simple linearly compact Lie superalgebras. Adv Math, 1998, 139: 1-55

DOI

2
Liu W D, He Y H. Finite-dimensional special odd Hamiltonian superalgebras in prime characteristic. Commun Contemp Math, 2009, 11(4): 523-546

DOI

3
Liu W D, Zhang Y Z. Infinite-dimensional modular odd Hamiltonian Lie superalgebras. Comm Algebra, 2004, 32: 2341-2357

DOI

4
Liu W D, Zhang Y Z. Finite-dimensional odd Hamiltonian superalgebras over a field of prime characteristic. J Aust Math Soc, 2005, 79: 113-130

DOI

5
Liu W D, Zhang Y Z, Wang X L. The derivation algebra of the Cartan-type Lie superalgebra HO. J Algebra, 2004, 273: 176-205

DOI

6
Strade H, Farnsteiner R. Modular Lie Algebras and Their Representations. New York: Marcel Dekker, 1988

7
Zhang Y Z, Fu H C. Finite-dimensional Hamiltonian Lie superalgebras. Comm Algebra, 2002, 30: 2651-2673

DOI

8
Zhang Y Z, Liu W D. Infinite-dimensional modular Lie superalgebras W and S of Cartan Type. Algebra Colloq, 2006, 132: 197-210

9
Zhang Y Z, Nan J Z. Finite-dimensional Lie superalgebras W(m, n, t) and S(m, n, t) of Cartan-type. Adv Math (China), 1998, 27: 240-246

Options
Outlines

/

〈 〉