The Grothendieck rings of finite dimensional representations of the basic classical Lie superalgebras are explicitly described in terms of the corresponding generalised root systems. We show that they can be interpreted as the subrings in the weight group rings invariant under the action of certain groupoids, which we call Weyl groupoids.

A bstract We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe “Orbifold groupoids” which control composition operations. Three-dimensional TQFT’s Dijkgraaf-Witten type will play an important role in analysis. briefly discuss extension to generalized symmetries applications constrain RG flows.

in this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. we show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

In this paper, we study a family of C*-subalgebras defined by fixed points generalized gauge actions Cuntz–Krieger algebra introducing étale groupoids whose associated C*-algebras are these C*-subalgebras. We show that topological conjugacy classes one-sided Markov shifts characterized in terms the isomorphism groupoids.

In this paper we use Quillen’s model structure given by Dwyer-Kan for the category of simplicial groupoids (with discrete object of objects) to describe in this category, in the simplicial language, the fundamental homotopy theoretical constructions of path and cylinder objects. We then characterize the associated left and right homotopy relations in terms of simplicial identities and give a si...

In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous representations of compact groupoids. We show that irreducible representationshave finite dimensional fibres. We prove the Schur’s lemma, Gelfand-Raikov theore...

Decompositions of the complete graph with n vertices Kn into edge disjoint cycles of length m whose union is Kn are commonly called w-cycle systems. Any m-cycle system gives rise to a groupoid defined on the vertex set of Kn via a well known construction. Here, it is shown that the groupoids arising from all m-cycle systems are precisely the finite members of a variety (of groupoids) for m = 3 ...

The main purpose of this paper is to develop new tools for the investigation of C-algebras which have been constructed from shift spaces in a series of papers by K. Matsumoto and T. Carlsen, cf. [Ma1]-[Ma5], [C], [CM]. The main results about the structure of these algebras which we obtain here give necessary and sufficient conditions for the algebras to be simple, and show that they all contain...