3 papers
math.CT2026
Yoshida algebra for groupoids
Keitaro Shiizuka
In this paper, we extend the notion of the Yoshida algebra of a finite group introduced in \cite{Yos83} to finite groupoids and investigate its fundamental properties. Our main res…
math.CT2026
Crossed Burnside rings for groupoids
Keitaro Shiizuka
In this paper, we extend the classical theory of crossed -sets and the crossed Burnside ring from a finite group to a finite groupoid . We introduce a natural m…
math.CT2026
Double coset for groupoids
Keitaro Shiizuka
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…