Related papers: Mackey formula for bisets over groupoids

Let $G$ be a finite group. In [HTW], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for $G$ and biset functors defined on subgroups of $G$ and bifree bisets as morphisms. This paper proposes a…

In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…

We give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups.

To study induced representation of some class of groups, Mackey's theory is very useful. In this paper, we consider some generalization of Mackey's theory for locally profinite groups. In particular, we give conditions on groups under which…

We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson…

In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…

In this paper, we shall establish the Mackey formulas in the following two set ups: (i) on the tensor induction and restriction functors on the modules over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard subalgebras of…

We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

We investigate the double cosets of a groupoid, focusing primarily on their enumeration, by means of two different approaches. The first approach extends the Cauchy-Frobenius lemma to groupoids and interprets it in terms of groupoid…

We derive double coset formulae for the genus and extended genus of a finitely generated nilpotent group G, using the notions of bounded and bounded above automorphisms of $\prod G_S$, which are defined relative to a fixed fracture square…

The rotation group is formulated based on the abstract $B(X)$-module framework. Although the infinitesimal generators of rotation group include differential operators, the rotation group is formulated utilizing the framework of bounded…

The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which…

Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…

We construct and describe a family of groupoids over complex curves which serve as the universal domains of definition for solutions to linear ordinary differential equations with singularities. As a consequence, we obtain a direct,…

We approach Mackenzie's LA-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds. There is a faithful functor from the category of LA-groupoids to the category of…

In this paper, a formula for the calculation of the number of right cosets contained in a double coset with respect to a unimodular group over a Dedekind domain is developed, and applications of this formula in the theory of congruence…

We develop the theory of Mackey profunctors, a version of Mackey functors for profinite groups.

In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad…

The aim of the paper is to establish a certain logic corresponding to lattice effect algebras. First, we answer a natural question whether a lattice effect algebra can be represented by means of a groupoid-like structure. We establish a…