Related papers: Finitely generated algebras with involution and th…
In this paper we answer two questions from [16], by showing that, over any algebraically closed field, $K$, there is a finitely generated, infinitely dimensional algebra $A$ such that algebras $A\otimes_{K}A$ and $A\otimes_{K} A^{op}$ are…
The paper is devoted to two new results concerning varieties of Leibnitz algebras over a field of the zero characteristic. Here is proved the sufficient condition for finiteness colength of variety of Leibnitz algebras. Here is also defined…
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
We prove the following. Let $R$ be a Noetherian ring, $B$ a finitely generated $R$-algebra, and $A$ a pure $R$-subalgebra of $B$. Then $A$ is finitely generated over $R$.
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
We study analogues of Tate's conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of abelian varieties without nontrivial…
We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite…
The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…
A base of a relatively free associative algebra with the identity x^3=0 over a field of arbitrary characteristic is found. As an application a minimal generating system of the 3x3 matrix invariant algebra is determined.
This paper addresses the classification problem of associative algebras over arbitrary base fields. We present a list of three-dimensional associative algebras with canonical representatives of the isomorphism classes for fields of…
We prove that all definable pre-orders are atomic, in a finitely generated free algebra of a discriminator variety of finite similarity type which is generated by its finite members.
We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…
Superspecies are introduced to provide the nice constructions of all finite-dimensional superalgebras. All acyclic superspecies, or equivalently all finite-dimensional (gr-basic) gr-hereditary superalgebras, are classified according to…
Over an arbitrary field of positive characteristic we construct an example of a locally finite variety of Lie algebras which does not have a finite basis of its polynomial identities. As a consequence we construct varieties of Lie algebras…
The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3x3 matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity x^3=0 is…
Given a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of…
We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…
There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we study similar notions for finite and profinite associative…
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…
To what extent does the maximal subfield spectrum of a division algebra determine the isomorphism class of that algebra? It has been shown that over some fields a quaternion division algebra's isomorphism class is largely if not entirely…