Yoshida algebra for groupoids
Abstract
In this paper, we extend the notion of the Yoshida algebra of a finite group introduced in Yos83 to finite groupoids and investigate its fundamental properties. Our main results show that the center of the Yoshida algebra of a finite groupoid is isomorphic to the center of the corresponding groupoid algebra, and that there exists a surjective ring homomorphism from the crossed Burnside ring of a finite groupoid, introduced in Shi26+, onto the center of the Yoshida algebra of a finite groupoid.
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