Related papers: Cross products, automorphisms, and gradings

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.

In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To prove this we study commutative subgroups of the group of…

We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…

We construct a 2-category of differential graded schemes. The local affine models in this theory are differential graded algebras, which are graded commutative with unit over a field of characteristic zero, are concentrated in non-positive…

A continuous family of non-outer conjugate aperiodic automorphisms whose crossed-products are all isomorphic is given on every interpolated free group factor. An explicit "duality" relationship between compact co-commutative Kac algebra…

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

The set of all subspaces of a given dimension in a finite classical polar space has a structure of a symmetric association scheme. If the dimension is zero, this is the scheme of the collinearity graph of the space; If the dimension is…

Let $X$ be a smooth complex projective curve, and let $x\in X$ be a point. We compute the automorphism group of the moduli space of framed vector bundles on $X$ of rank $r \geq 2$ with a framing over $x$. It is shown that this automorphism…

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.

We consider the problem of classifying gradings by groups on a finite-dimensional algebra $A$ (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…

We classify the automorphism groups of del Pezzo surfaces of degrees one and two over an algebraically closed field of characteristic two. This finishes the classification of automorphism groups of del Pezzo surfaces in all characteristics.

First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an…

For 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…

We obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$.…

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…