Related papers: Cayley unitary elements in group algebras under or…

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…

Let $G$ be a finite group, $H \le G$ a subgroup, $R$ a commutative ring, $A$ an $R$-algebra, and $\alpha$ an action of $G$ on $A$ by $R$-algebra automorphisms. We study the associated \emph{skew Hecke algebra}…

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $G$ be a algebraic $K$-group. Given two algebraic morphisms $\varphi:X\rightarrow G$ and $\psi:Y\rightarrow G$, we define their convolution…

We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…

It is well known that for any finite Galois extension field $K/F$, with Galois group $G = \mathrm{Gal}(K/F)$, there exists an element $\alpha \in K$ whose orbit $G\cdot\alpha$ forms an $F$-basis of $K$. Such an element $\alpha$ is called…

An element of a group is called \emph{reversible} if it is conjugate to its inverse. While reversibility in the quaternionic M\"{o}bius group $\mathrm{PSL}(2,\mathbb{H})$ has traditionally been studied using geometric and dynamical methods,…

Let $V$ be a finite-dimensional vector space over the field with $p$ elements, where $p$ is a prime number. Given arbitrary $\alpha,\beta\in \mathrm{GL}(V)$, we consider the semidirect products $V\rtimes\langle \alpha\rangle$ and…

Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…

Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference…

For a locally compact abelian group $G$, J. L. Taylor (1971) gave a complete characterization of invertible elements in the measure algebra $M(G)$. Using the Fourier-Stieltjes transform, this characterization can be carried out in the…

The reduced norm-one group G of a central simple algebra is an inner form of the special linear group, and an involution on the algebra induces an automorphism of G. We study the action of such automorphisms in the cohomology of arithmetic…

Cayley's theorem tells us that all groups $\mathbf{G}$ occur as subgroups of the group of automorphisms over some set $X$. In this paper we consider a `sort-of' converse to this question: given a set $X$ and some transformation group…

Let $G$ be a finite group. For each $m>1$ we define the symmetric canonical subset $S=S(m)$ of the Cartesian power $G^m$ and we consider the family of Cayley graphs $\mathscr{G}_m(G)=Cay(G^m,S)$. We describe properties of these graphs and…

We consider the moduli space $\mathcal{M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a complex semisimple Lie group. This is a hyperk\"ahler manifold homeomorphic to the moduli space $\mathcal{R}(G)$ of…

Let $G$ be a finite group acting on an ice quiver with potential $(Q, F, W)$. We construct the corresponding $G$-equivariant relative cluster category and $G$-equivariant Higgs category, extending the work of Demonet. Using the orbit…

We review the properties of transversality of distributions with respect to submersions. This allows us to construct a convolution product for a large class of distributions on Lie groupoids. We get a unital involutive algebra…

A finite group $G$ admits an {\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend…

Let $\mathcal{M}(n)$ be the subgroup of $GL(n,\mathbb{Z})$ generated by the particular involutions that are identical to the identity, except for a single line where $-1$ and $+1$ alternate. We study the properties of $\mathcal{M}(n)$, and…

The one-parameter family of second order nonlinear difference equations each of which is given by $$ x_{n-1}x_nx_{n+1}=x_{n-1}+(x_n)^{\beta-1}+x_{n+1} \qquad(\beta\in\mathbb{N}) $$ is explored. Since the equation above is arising from seed…

Suppose $R$ is a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ such that $q+q^{-1}$ is invertible. For an oriented surface $\Sigma$, let $\mathcal{S}(\Sigma;R)$ denote the Kauffman bracket skein algebra of…