Mikhail Kochetov
Group gradings on finitary simple Lie algebras.
Wed, 06/15/2011 - 15:01 — SomNambulAuthors: Yuri Bahturin, Mikhail Kochetov, Matej Brešar
Subjects: Rings and Algebras
AbstractWe 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.Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra.
Thu, 09/09/2010 - 15:01 — SomNambulAuthors: Mikhail Kochetov, Alberto Elduque
Subjects: Rings and Algebras
AbstractGiven a grading $\Gamma: A=\oplus_{g\in G}A_g$ on a nonassociative algebra
$A$ by an abelian group $G$, we have two subgroups of the group of
automorphisms of $A$: the automorphisms that stabilize each homogeneous
component $A_g$ (as a subspace) and the automorphisms that permute the
components. By the Weyl group of $\Gamma$ we mean the quotient of the latter
subgroup by the former. In the case of a Cartan decomposition of a semisimple
complex Lie algebra, this is the automorphism group of the root system, i.e.,
the so-called extended Weyl group.Group gradings on restricted Cartan type Lie algebras.
Tue, 01/05/2010 - 16:01 — SomNambulAuthors: Yuri Bahturin, Mikhail Kochetov
Subjects: Rings and Algebras
AbstractFor a given abelian group G, we classify the isomorphism classes of
G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1)
(m>=2), in terms of numerical and group-theoretical invariants. Our main tool
is automorphism group schemes, which we determine for the simple restricted Lie
algebras of types S(m;1) and H(m;1). The ground field is assumed to be
algebraically closed of characteristic p>3.
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