Let g be any finite-dimensional odd Contact superalgebra over a field of prime characteristic. By means of determining the minimal dimensions of image spaces of certain inner superderivations, it is proved that the principal filtration of g is invariant under the automorphisms of g. Then, the parameters by which g is defined are proved to be intrinsic and thereby the odd Contact superalgebras are classified up to isomorphisms. Furthermore, the restrictedness of g is determined and the automorphism group of g in restrictedness case is proved to be isomorphic to the admissible automorphism group of the underlying superalgebra of g under a concrete isomorphism Φ. Further properties of Φ are given and as an application, the results above are used to discuss the p-characters of the irreducible representations for g.
1
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
Yan Chen; Wende Liu. Finite-Dimensional Odd Contact Superalgebras over a Field of Prime Characteristic. Journal of Lie Theory, Tome 21 (2011) no. 3, pp. 729-754. http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a4/
@article{JOLT_2011_21_3_a4,
author = {Yan Chen and Wende Liu},
title = {Finite-Dimensional {Odd} {Contact} {Superalgebras} over a {Field} of {Prime} {Characteristic}},
journal = {Journal of Lie Theory},
pages = {729--754},
year = {2011},
volume = {21},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a4/}
}
TY - JOUR
AU - Yan Chen
AU - Wende Liu
TI - Finite-Dimensional Odd Contact Superalgebras over a Field of Prime Characteristic
JO - Journal of Lie Theory
PY - 2011
SP - 729
EP - 754
VL - 21
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a4/
ID - JOLT_2011_21_3_a4
ER -
%0 Journal Article
%A Yan Chen
%A Wende Liu
%T Finite-Dimensional Odd Contact Superalgebras over a Field of Prime Characteristic
%J Journal of Lie Theory
%D 2011
%P 729-754
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a4/
%F JOLT_2011_21_3_a4
