54 research outputs found
Lie Superautomorphisms on Associative Algebras, II
Lie superautomorphisms of prime associative superalgebras are considered. A
definitive result is obtained for central simple superalgebras: their Lie
superautomorphisms are of standard forms, except when the dimension of the
superalgebra in question is 2 or 4.Comment: 19 pages, accepted for publication in Algebr. Represent. Theor
Braided m-Lie Algebras
Braided m-Lie algebras induced by multiplication are introduced, which
generalize Lie algebras, Lie color algebras and quantum Lie algebras. The
necessary and sufficient conditions for the braided m-Lie algebras to be strict
Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras
are given, which are generalized matrix braided m-Lie algebras and braided
m-Lie subalgebras of , where is a Yetter-Drinfeld module over
with dim . In particular, generalized classical braided m-Lie
algebras and of
generalized matrix algebra are constructed and their connection with
special generalized matrix Lie superalgebra
and orthosymplectic generalized matrix Lie super algebra are established. The relationship between representations
of braided m-Lie algebras and their associated algebras are established.Comment: 14 page
Group gradings on finitary simple Lie algebras
We classify, up to isomorphism, all gradings by an arbitrary abelian group on
simple finitary Lie algebras of linear transformations (special linear,
orthogonal and symplectic) on infinite-dimensional vector spaces over an
algebraically closed field of characteristic different from 2.Comment: Several typographical errors have been correcte
Group Gradings on Associative Algebras with Involution
AbstractIn this paper we describe the group gradings by a finite abelian group G of the matrix algebra Mn(F) over an algebraically closed field F of characteristic different from 2, which respect an involution (involution gradings). We also describe, under somewhat heavier restrictions on the base field, all G-gradings on all finite-dimensional involution simple algebras
Schreier rewriting beyond the classical setting
Using actions of free monoids and free associative algebras, we establish
some Schreier-type formulas involving the ranks of actions and the ranks of
subactions in free actions or Grassmann-type relations for the ranks of
intersections of subactions of free actions. The coset action of the free group
is used to establish the generalization of the Schreier formula to the case of
subgroups of infinite index. We also study and apply large modules over free
associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V.,
Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008),
753 - 759.Comment: 17 page
Filtered multiplicative bases of restricted enveloping algebras
We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie
algebra over a field of positive characteristic p
- …