Related papers: (Co)-Induced Two Crossed Modules

In this paper, we define the notion of induced representations of a Hilbert $C^{*}$-module and we show that Morita equivalence of two Hilbert modules (in the sense of Moslehian and Joita), implies the equivalence of categories of…

For a finite dimensional Hopf algebra we show that an associated natural inclusion of infinite crossed products is the crossed product by the Drinfeld double, and that this is a characterisation of the double.

We introduce the notion of a cross-frame potential function, which takes one frame as input and returns its cross-frame potential value with respect to another frame. We analyze the behavior of this new function to determine what…

The Hochschild and (cotriple) cyclic homologies of crossed modules of (not-necessarily-unital) associative algebras are investigated. Wodzicki's excision theorem is extended for inclusion crossed modules in the category of crossed modules…

The notion of retrocell in a double category with companions is introduced and its basic properties established. Explicit descriptions in some of the usual double categories are given. Monads in a double category provide an important…

We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.

We present a theory for two recent experiments in bulk strained semiconductors \cite{kato1, kato2} and show that a new, previously overlooked, strain spin-orbit coupling term may play a fundamental role. We propose simple experiments that…

We introduce the notion of a braiding on a skew monoidal category, whose curious feature is that the defining isomorphisms involve three objects rather than two. These braidings are shown to arise from, and classify, cobraidings (also known…

We consider a framework for representing double loop spaces (and more generally E-2 spaces) as commutative monoids. There are analogous commutative rectifications of braided monoidal structures and we use this framework to define iterated…

Given a finite dimensional algebra $A$, we consider certain sets of idempotents of $A$, called self-injective cores, to which we associate 2-subcategories of the 2-category of projective bimodules over $A$. We classify the simple transitive…

The subject of this article are cross product bialgebras without co-cycles. We establish a theory characterizing cross product bialgebras universally in terms of projections and injections. Especially all known types of biproduct, double…

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call,…

In this paper, we will construct the injective resolution of any $\cR$-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in ($\cR$-2-Mod).

In this work, we explain `Peiffer pairings' in the Moore (bi)complex of a bisimplicial group and give their applications for crossed modules and crossed squares.

In this paper, we state the notion of morphisms in the category of abelian crossed modules and prove that this category is equivalent to the category of strict Picard categories and regular symmetric monoidal functors. The theory of…

A new model of two coupled neurons is presented by the partly diffusive Hindmarsh-Rose equations. The solution semiflow exhibits globally absorbing characteristics. As the main result, the self-synchronization of the coupled neurons at a…

Advances in manipulating the structure of optical beams enable the study of interaction between structured light and low-dimensional semiconductor systems. We explore the photocurrents in two-dimensional systems excited by such…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double…

We study the class of equimultiple modules. In particular, we prove several criteria for an equimultiple module to be a complete intersection and prove the openness of the equimultiple locus of an ideal module.