We obtain some explicit calculations of crossed Q modules induced from a crossed module over a normal subgroup P of Q By virtue of theorems of Brown and Higgins this enables the computation of the homotopy types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups Introduction A crossed module M M P has a classifying space BM see for example ...

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre’s problem, was extensively studied befo...

In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. other words, construct product, pullback and equalizer objects in racks. We therefore unify group-theoretical analogy completeness property sense functor $\mathbf{Conj \colon Grp \to Rack} $.

In [HL1]–[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We show in the present paper that for any vertex operator algebra containing a vertex operator subalgebra isomorphic to a tensor product algebra of minimal Virasoro vertex oper...

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov pro...

We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere.