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We describe the automorphism groups of elliptic Poisson algebras on polynomial algebras in three variables and give an explicit set of generators and defining relations for this group.
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their…
The purpose of this paper is to study the structure of Lotka-Volterra algebras, the set of their idempotent elements and their group of automorphisms. These algebras are defined through antisymmetric matrices and they emerge in connection…
We determine the structure of Leavitt path algebras of polynomial growth and discuss their automorphisms and involutions.
We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible structures on the strictly upper triangular matrix algebra $UT_n(K)$ for all $n\ge 3$.
Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.
Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. It is shown that correlation…
Various spaces of symmetries of a structure are naturally endowed with both an algebraic and a topological structure. For example, the automorphism group of a structure is, on top of being a group, a topological group when equipped with the…
We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a…
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
A procedure for the algebraization of a $CR$-manifold and its holomorphic automorphisms is described. Examples of the application of algebraization are considered. Questions arising in connection with the algebraization of a $CR$-manifold…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…