Related papers: Azumaya Algebras With Orthogonal Involution Admitt…

Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…

A classic result of representation theory is Brauer's construction of a diagrammatical (geometrical) algebra whose matrix representation is a certain given matrix algebra, which is the commutating algebra of the enveloping algebra of the…

Let $R$ be a ring with $char(R)\neq2$ whose unit group are denoted by $\mathcal{U}(R)$, $G$ a group, and $RG$ its group ring. Let $*$ be an involution in $G$, $\sigma:G\rightarrow\mathcal{U}(R)$ be a nontrivial group homomorphism, with…

Suppose that ${\mathcal A}$ is an algebra, $\sigma,\tau:{\mathcal A}\to{\mathcal A}$ are two linear mappings such that both $\sigma({\mathcal A})$ and $\tau({\mathcal A})$ are subalgebras of ${\mathcal A}$ and ${\mathcal X}$ is a…

We define a trivolution on a complex algebra $A$ as a non-zero conjugate-linear, anti-homomorphism $\tau$ on $A$, which is a generalized inverse of itself, that is, $\tau^3=\tau$. We give several characterizations of trivolutions and show…

Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then…

An involution $#$ on an associative ring $R$ is \textit{formally real} if a sum of nonzero elements of the form $r^# r$ where $r \in R$ is nonzero. Suppose that $R$ is a central simple algebra (i.e. $R=M_n(D)$ for some integer $n$ and…

Let $\mathcal A$ be a unital algebra equipped with an involution $(\cdot)^\dagger$, and suppose that the multiplicative set $\mathcal S\subseteq \mathcal A$ generated by the elements of the form $1 + a^\dagger a$ satisfies the Ore…

The main goal of this paper is to compare the silting theory of an $R$-algebra $\Lambda$ over a Noetherian ring $R$ with that of its tensor product $\Lambda \otimes \Gamma$ with another $R$-algebra $\Gamma$. In the case that the $R$-algebra…

All isometries $\sigma$ in a quadratic space over a non-archimedean local field of characteristic not 2 satisfying that any isometry $\tau$ which is conjugate to $\sigma$ in the general linear group is conjugate to $\sigma$ in the…

For any factorization domain $\cal A$ and an algebra endomorphism $\sigma$ of $\cal A$, there exists a non-associative algebra $({\cal A},\sigma,[\cdot,\cdot])$ with multiplication satisfying skew-symmetry and generalized (twisted) Jacobi…

Given a reduced local algebra $T$ over a suitable ring or field $k$ we study the question of whether there are nontrivial algebra surjections $R\to T$ which induce isomorphisms $\Omega_{R/k}\otimes T \to \Omega_{T/k}$. Such maps, called…

In a previous work we established a super Schur-Weyl-Brauer duality between the orthosymplectic supergroup of superdimension $(m|2n)$ and the Brauer algebra with parameter $m-2n$. This led to a proof of the first fundamental theorem of…

We extend the integrability analysis for scalar evolution equations of type $$u_t=u_m+f(u,u_1,...,u_{m-1})$$ from the case that the right hand side is a $\lambda$-homogeneous formal power series to the case that it is a nonhomogeneous…

The crystalline differential operators on a smooth variety X give rise to a non-split Azumaya algebra over the cotangent bundle of the Frobenius twist X'. In some cases, this Azumaya algebra splits when restricted to finite covers of X'. In…

Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted $\mathcal{A}$ and $\mathcal{B}$) that are constructed from a nondegenerate quasihomogeneous polynomial $W$ and a related group of symmetries…

Let $K$ be an algebraically closed field of characteristic zero, and let $A$ and $B$ be two simple algebras with involution over $K$. In this note we study the embedding problem for algebras with involution. More specifically, if the…

Let $G$ be a group with involution * and $\sigma\colon G\to\{\pm1\}$ a group homomorphism. The map $\sharp$ that sends $\alpha=\sum\alpha_gg$ in a group ring $RG$ to $\alpha^{\sharp}=\sum\sigma(g)\alpha_gg^*$ is an involution of $RG$ called…

An irreducible module for the parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$ is said to be of $\sigma$-type if an automorphism of the fusion algebra of $K(\mathfrak{sl}_2,k)$ of order $k$ is trivial on it. For any integer $k \ge…

For a smooth projective surface $X$ satisfying $H_1(X,\mathbb{Z}) = 0$ and $w \in H^2(X,\mu_r)$, we study deformation invariants of the pair $(X,w)$. Choosing a Brauer-Severi variety $Y$ (or, equivalently, Azumaya algebra $\mathcal{A}$)…