相关论文: Twisted Exponents and Twisted Frobenius-Schur Indi…

In an attempt to understand the origin of post groups introduced by C. Bai, L. Guo, Y. Sheng, R. Tang, from the perspective of rings, we introduce the notion of (weak) twisted post groups. First, we show that every element in a twisted post…

In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod $p$ formula for the twisted Alexander polynomial of a knot in the $3$-sphere associated…

In this paper we show that for an important class of non-trivial Hopf algebras, the Schur indicator is a computable invariant. The Hopf algebras we consider are all abelian extensions; as a special case, they include the Drinfeld double of…

We construct a two dimensional unoriented open/closed topological field theory from a finite graded group $\pi:\hat{G} \twoheadrightarrow \{1,-1\}$, a $\pi$-twisted $2$-cocycle $\hat{\theta}$ on $B \hat{G}$ and a character $\lambda: \hat{G}…

The goal of this paper is to construct a calculus whose higher indices are naturally elements in the twisted K-theory groups for Lie groupoids. Given a Lie groupoid $G$ and a $PU(H)$-valued groupoid cocycle, we construct an algebra of…

We extend recent work by Howie, Mathews and Purcell to simplify the calculation of A-polynomials for any family of hyperbolic knots related by twisting. The main result follows from the observation that equations defining the deformation…

This expository article presents a unified ring theoretic approach, based on the theory of Frobenius algebras, to a variety of results on Hopf algebras. These include a theorem of S. Zhu on the degrees of irreducible representations, the…

In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The conditions on partial cocycles are established…

The twisted Alexander polynomial of a knot is defined associated to a linear representation of the knot group. If there exists a surjective homomorphism of a knot group onto a finite group, then we obtain a representation of the knot group…

We give an explicit description, up to gauge equivalence, of group-theoretical quasi-Hopf algebras. We use this description to compute the Frobenius-Schur indicators for group-theoretical fusion categories.

If G is a finite group and k is a field, there is a natural construction of a Hopf algebra over k associated to G, the Drinfel'd double D(G). We prove that if G is any finite real reflection group with Drinfel'd double D(G) over an…

Let $p$ be an odd prime and let $B$ be a $p$-block of a finite group which has cyclic defect groups. We show that all exceptional characters in $B$ have the same Frobenius-Schur indicators. Moreover the common indicator can be computed,…

We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from…

We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group…

The present article is devoted to studying the categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras, introduced by Wang (2023), and weak twisted relative Rota-Baxter operators. The latter objects…

In this note we prove a generalization of the Frobenius-Schur theorem for finite groups for the case of semisimple Hopf algebra over an algebraically closed field of characteristic 0. A similar result holds in characteristic $p > 2$ if the…

Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…

Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is…

Recall (math.QA/9812151) that the exponent of a finite-dimensional complex Hopf algebra H is the order of the Drinfeld element u of the Drinfeld double D(H) of H. Recall also that while this order may be infinite, the eigenvalues of u are…

In this paper, we obtain a canonical central element $\nu_H$ for each semi-simple quasi-Hopf algebra $H$ over any field $k$ and prove that $\nu_H$ is invariant under gauge transformations. We show that if $k$ is algebraically closed of…