Related papers: Quasi-semisimple elements

To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with…

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…

Let $G$ be a nontrivial transitive permutation group on a finite set $\Omega$ and recall that an element of $G$ is a derangement if it has no fixed points. Derangements always exist by a classical theorem of Jordan, but there are so-called…

The quasi-partition algebras were introduced by Daugherty and the first author as centralizers of the symmetric group. In this article, we give a more general definition of these algebras and give a construction of their simple modules. In…

We study varieties of semigroups related to completely 0-simple semigroup. We present here an algorithmic descriptions of these varieties interms of "forbidden" semigroups.

This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…

We apply a general approach for distributions of binary isolating and semi-isolating formulas to families of isolated types and to the class of countably categorical theories.

Suppose that $\tilde{G}$ is a connected reductive group defined over a field $k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the…

Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u in G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the…

For a simple algebraic group $G$ over an algebraically closed field, we study products of normal subsets. For this we mark the nodes of the Dynkin diagram of $G$. We use two types of labels, a binary marking and a labeling with non-negative…

We show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split.

Let $D$ be a connected component of a possibly disconnected reductive group $G$ over an algebraic closed field. We define a partition of $D$ into finitely many Strata each of which is a union of $G^0$-conjugacy classes of fixed dimension.…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

This work completes the classification of the imprimitive irreducible modules, over algebraically closed fields of characteristic 0, of the finite quasisimple groups.

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…

With any non necessarily orientable unpunctured marked surface (S,M) we associate a commutative algebra, called quasi-cluster algebra, equipped with a distinguished set of generators, called quasi-cluster variables, in bijection with the…

A semi-algebraic set is a subset of $\mathbb{R}^n$ defined by a finite collection of polynomial equations and inequalities. In this paper, we investigate the problem of determining whether two points in such a set belong to the same…

Given a finite group $G$, the solubilizer of an element $x$, denoted by $\Sol_G(x)$, is the set of all elements $y$ such that $\langle x, y\rangle$ is a soluble subgroup of $G$. In this paper, we provide a classification for all…

Double Bruhat cells in a semisimple group are intersections of cells in two Bruhat decompositions corresponding to two opposite Borel subgroups. They form a geometric framework for the study of total positivity in semisimple groups; they…

This paper is a continuation of the theory of cyclic elements in semisimple Lie algebras, developed by Elashvili, Kac and Vinberg. Its main result is the classification of semisimple cyclic elements in semisimple Lie algebras. The…