Yury Volkov

Degenerations of binary Lie and nilpotent Malcev algebras

ABSTRACT We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ℂ. In particular, we describe all irreducible components of these varieties.

Degenerations of Zinbiel and nilpotent Leibniz algebras

ABSTRACT We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over In particular, we describe all irreducible components in the corresponding varieties.

Conservative algebras of 2-dimensional algebras, II

ABSTRACT In 1990 Kantor defined the conservative algebra W(n) of all algebras (i.e. bilinear maps) on the n-dimensional vector space. If n>1, then the algebra W(n) does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). We describe automorphisms, one-sided ideals, and idempotents of W(2). Also similar problems are solved for the algebra W2 of all commutative algebras on the 2-dimensional vector space and for the algebra S2 of all commutative algebras with trace zero multiplication on the 2-dimensional vector space.

Stable Calabi–Yau dimension of self-injective algebras of finite type

Abstract We give an equivalent definition of the stable Calabi–Yau dimension in terms of bimodule syzygies and so-called stably inner automorphisms. Using it, we complete the computation of the stable Calabi–Yau dimensions of the self-injective algebras of finite representation type which was started by K. Erdmann, A. Skowronski, J. Bialkowski and A. Dugas.

On Standard Derived Equivalences of Orbit Categories

Let k be a commutative ring, A

Generating degrees for graded projective resolutions

\mathcal {A}

Külshammer Ideals of Graded Categories and Hochschild Cohomology

and ℬ

The variety of 2-dimensional algebras over an algebraically closed field

\mathcal {B}

The geometric classification of Leibniz algebras

– two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ

BV structure on Hochschild cohomology of the group ring of quaternion group of order eight in characteristic two

\mathcal {K}_{p}^{\mathrm {b}}\mathcal {B}