Deformations of classical Lie algebras

Deformations of Symmetric Simple Modular Lie (Super)Algebras

“…In several papers [31,32,33,78,90,92], with difficult results clearly explained, N. Chebochko, and her scientific advisor, M. Kuznetsov, gave an overview of the situation for Lie algebras of the form g(A) and g(A) (i) /c. In [32], Chebochko writes (footnotes are ours): "According to [40], for p = 3, the Lie algebra C 2 is the only algebra among the series A n , B n , C n , D n that admits nontrivial deformations.…”

Global deformations of a Lie algebra of type $\bar{A_5}$

“…The space W ⊗ W is that of all bilinear functions on W * . Denote by S (2) (W ) the module of symmetric functions. Obviously, Λ 2 W ⊂ S (2) (W ) ⊂ W ⊗ W and all embeddings considered are consistent with the action of GL(V ).…”

“…Denote by S (2) (W ) the module of symmetric functions. Obviously, Λ 2 W ⊂ S (2) (W ) ⊂ W ⊗ W and all embeddings considered are consistent with the action of GL(V ). Besides, S (2) (W ) = Λ 2 W ⊕ < e i e j e k ⊗ e i e j e k , i < j < k > .…”

“…Classical Lie algebras over fields of characteristic zero and characteristic p > 3 are rigid (see [1]). In [2], [3] it is proved that over fields of characteristic p > 2 only algebras of type C 2 have non-trivial deformations, their description is given in [4], [5]. At present there does not seem to exist any complete de-scription of deformations of classical Lie algebras of characteristic 2 and Lie algebras of their derivations.…”

Towards classification of simple finite dimensional modular Lie superalgebras

“…Having obtained a supply of such examples, we can sit down to c o m p u t e c e r t a i n c o h o m o l o g y i n o r d e r t o d e s c r i b e t h e i r d e f o rm a t i o n s (provided we will be able to understand what we are computing, cf. footnote 2); for the already performed, see [KKCh,KuCh,Ch,BGL4].…”