Related papers: Partial actions: What they are and why we care
In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph…
Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.
This is an expository article developing some aspects of the theory of categorical actions of Kac-Moody algebras in the spirit of works of Chuang-Rouquier, Khovanov-Lauda, Webster, and many others.
This document aims to give a self-contained account of the parts of abelian group theory that are most relevant for algebraic topology. It is almost purely expository, although there are some slightly unusual features in the treatment of…
The interplay between the Hamilton-Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.
Let $\mathbb{k}$ be an algebraically closed field of characteristic zero. Let $D$ be a division algebra of degree $d$ over its center $Z(D)$. Assume that $\mathbb{k}\subset Z(D)$. We show that a finite group $G$ faithfully grades $D$ if and…
We present a extension of the classical open mapping principle and Effros' theorem for Polish group actions to the context of partial group actions.
We construct approximately inner actions of discrete amenable groups on strongly amenable subfactors of type II_1 with given invariants, and obtain classification results under some conditions. We also study the lifting of the relative \chi…
n^{th} root of a Lie algebra and its dual (that is fractional supergroup) based on the permutation group $S_n$ invariant forms are formulated in the Hopf algebra formalism. Detailed discussion of $S_3$-graided $sl(2)$ algebras is done.
We give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic…
This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…
We study the problem of constructing a globalization for partial actions on *-algebras, C*-algebras and Hilbert modules. For the first ones we give a necessary condition for the existence of a globalization and we prove this conditions is…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
We investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
This article focuses on those aspects about partial actions of groups which are related to Schur's theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by…
We give the basic definitions of group actions on (algebraic) stacks, and prove the existence of fixed points and quotients as (algebraic) stacks.
This is a survey of results that extend notions of the classical invariant theory of linear actions by finite groups on $k[x_1, \dots, x_n]$ to the setting of finite group or Hopf algebra $H$ actions on an Artin-Schelter regular algebra…
The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…
Recent results of L. Zsido, based on his previous work with C. P. Niculescu and A. Stroh, on actions of topological semigroups on von Neumann algebras, give a Jacobs-de Leeuw-Glicksberg splitting theorem at the von Neumann algebra (rather…
In this paper, we construct a partial group \(\mathcal{P}(F)\) that represents the "partial symmetry" inherent in a subset \(F\) of \(d\)-dimensional Euclidean space. In cases where \(F\) is not connected, \(\mathcal{P}(F)\) captures more…