Convolution algebras for Relational Groupoids and Reduction

Abstract

We introduce the notions of relational groupoids and relational convolution algebras. We provide various examples arising from the group algebra of a group $G$ and a given normal subgroup $H$. We also give conditions for the existence of a Haar system of measures on a relational groupoid compatible with the convolution, and we prove a reduction theorem that recovers the usual convolution of a Lie groupoid.

27 pages, 1 figure. To appear in Pacific Journal of Mathematics

References in corpus (7)

• Perturbative quantum gauge theories on manifolds with boundary
• Introduction to the BV-BFV formalism
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• Relational Symplectic Groupoid Quantization for Constant Poisson Structures
• Frobenius objects in the category of relations
• Split Canonical Relations