相关论文: Algebras of conjugacy classes of partial elements

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer…

In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras of conjugacy classes of symmetric groups $S_n$ admit a stabilization (in a non-obvious sense) as $n\to \infty$. We extend their construction to a class of pairs of…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We…

Bakalov, Kac and Voronov introduced Leibniz conformal algebras (and their cohomology) as a non-commutative analogue of Lie conformal algebras. Leibniz conformal algebras are closely related to field algebras which are non-skew-symmetric…

We generalize the concept of partial permutations of Ivanov and Kerov and introduce $k$-partial permutations. This allows us to show that the structure coefficients of the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$…

Let $G$ be a group. Two elements $x, y$ are said to be {\it $z$-equivalent} if their centralizers are conjugate in $G$. The class equation of $G$ is the partition of $G$ into conjugacy classes. Further decomposition of conjugacy classes…

In this paper, we construct a combinatorial algebra of partial isomorphisms that gives rise to a "projective limit" of the centers of the group algebras C[GL(n,Fq)]. It allows us to prove a GL(n,Fq)-analogue of an old theorem of Farahat and…

Let $S(\infty)$ denote the infinite symmetric group formed by the finitary permutations of the set of natural numbers; this is a countable group. We introduce its virtual group algebra, a completion of the conventional group algebra…

Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a…

Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the…

We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…

We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of…

Infinite-dimensional universal Cardy-Frobenius algebra is constructed, which unifies all particular algebras of closed and open Hurwitz numbers and is closely related to the algebra of differential operators, familiar from the theory of…

This is an introduction to the group algebras of the symmetric groups, written for a quarter-long graduate course. After recalling the definition of group algebras (and monoid algebras) in general, as well as basic properties of…

We give classifications of group gradings, up to equivalence and up to isomorphism, on the tensor product of a Cayley algebra $\mathcal{C}$ and a Hurwitz algebra over a field of characteristic different from 2. We also prove that the…

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which…

In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…

The Jucys-Murphy elements for wreath products G_n associated to any finite group G are introduced and they play an important role in our study on the connections between class algebras of G_n for all n and vertex algebras. We construct an…