Related papers: Superinvolutions on block-triangular matrix algebr…

We consider a superalgebra with a superinvolution or graded involution $\#$ over a field $F$ of characteristic zero and assume that it is a $PI$-algebra. In this paper, we present the proof of a version of the celebrated hook theorem…

We introduce superequivalence and superuniform spaces.

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…

An automorphism group of an incidence structure I induces a tactical decomposition on I. It is well known that tactical decompositions of t-designs satisfy certain necessary conditions which can be expressed as equations in terms of the…

We introduce a new class of algebras called endo-commutative algebras in which the square mapping preserves multiplication, and provide a complete classification of endo-commutative algebras of dimension 2 over the field F_2 of two…

We consider the problem of characterizing upper-triangular matrices $M=\begin{pmatrix}p&r\\0&q\end{pmatrix}\in M_2(\mathbb Z)$ which can be represented in the form $A^2-B^2$ with upper-triangular integer matrices $A$ and $B$ and give a…

We provide upper bounds on the u-invariant for skew-hermitian forms over a quaternion algebra with its canonical involution in terms of the u-invariant of the base field F of characteristic different from 2 when I^3F = 0.

Buan, Iyama, Reiten and Smith proved that cluster-tilting objects in triangulated 2-Calabi--Yau categories are closely connected with mutation of quivers with potentials over an algebraically closed field. We prove a more general statement…

We describe supertraces on ``queerifications'' (see arxiv:2203.06917) of the algebras of matrices of ``complex size'', algebras of observables of Calogero-Moser model, Vasiliev higher spin algebras, and (super)algebras of…

We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.

An orthogonal involution $\sigma$ on a central simple algebra $A$, after scalar extension to the function field $\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_\sigma$ over $\mathcal{F}(A)$, which is…

This monograph starts with an upper triangular matrix with integer entries and 1's on the diagonal. It develops from this a spectrum of structures, which appear in different contexts, in algebraic geometry, representation theory and the…

In this paper, a classification of modules of the intermediate series over the twisted N=2 superconformal algebra is obtained.

This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case which was left open in previous papers) and that three…

We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite…

In this paper we describe all, up to isomorphism, left unital, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and $\mathbb{R}$. We tabulate the algebras with the units.

We develop a formalism of poly-vector deformations for Type IIB backgrounds with a block diagonal metric and non-vanishing self-dual 5-form RR field strength. Making use of the embedding of the Type IIB theory into the $\mathrm{E}_{6(6)}$…

We investigate the structure of maximal commutative subalgebras of the finite dimensional Grassmann algebra over a field of characteristic different from two.