Müller generalized in [12] the notion of a Frobenius extension to left (right) quasi-Frobenius extension and proved the endomorphism ring theorem for these extensions. Recently, Guo observed in [9] that for a ring homomorphism φ : R → S, the restriction of scalars functor has to induction functor S ⊗R − : RM → SM as right ”quasi” adjoint if and only if φ is a left quasi-Frobenius extension. In ...

For the general linear group GLn(k) over an algebraically closed field k of characteristic p, there are two types of “twisting” operations that arise naturally on partitions. These are of the form λ → pλ and λ → λ+ prτ The first comes from the Frobenius twist, and the second arises in various tensor product situations, often from tensoring with the Steinberg module. This paper surveys and adds ...

We define generalized Frobenius-Schur indicators for objects in a linear pivotal category C. An equivariant indicator of an object is defined as a functional on the Grothendieck algebra of the quantum double Z(C) of C using the values of the generalized Frobenius-Schur indicators. In a spherical fusion category C with Frobenius-Schur exponent N , we prove that the set of all equivariant indicat...

In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra H via the categorical counterpart developed in a 2005 preprint. When H is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of H such that...

This article is divided into two parts. In the first part we work over a field k and prove that Frobenius space associated to algebra generated as left A-module by coproduct. particular, dimension coincides with of algebra. second commutative ring We introduce concept nearly algebras in this context construct solutions quantum Yang-Baxter equation starting from elements space. Also, give an alt...

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.

A subalgebra pair of semisimple complex algebras B ⊆ A with inclusion matrix M is depth two if MM t M ≤ nM for some positive integer n and all corresponding entries. If A and B are the group algebras of finite group-subgroup pair H < G, the induction-restriction table equals M and S = MM t satisfies S 2 ≤ nS iff the subgroup H is depth three in G; similarly depth n > 3 by successive right multi...

The statistical properties of endomorphisms under the assumption that the associated Perron– Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak mixing, and exactness....