Convolution algebras for relational groupoids and reduction

@article{Contreras2021ConvolutionAF,
  title={Convolution algebras for relational groupoids and reduction},
  author={Iv{\'a}n A. Contreras and Nima Moshayedi and Konstantin Wernli},
  journal={Pacific Journal of Mathematics},
  year={2021}
}
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. 

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References

SHOWING 1-10 OF 46 REFERENCES
Conditioning as disintegration
TLDR
Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning, but in print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.
A Path Integral Approach¶to the Kontsevich Quantization Formula
Abstract: We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path
A Groupoid Approach to Quantization
Many interesting $C∗$-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution $C∗$-algebra of a symplectic
Relational Symplectic Groupoids
This note introduces the construction of relational symplectic groupoids as a way to integrate every Poisson manifold. Examples are provided and the equivalence, in the integrable case, with the
Frobenius objects in the category of spans
We consider Frobenius objects in the category Span, where the objects are sets and the morphisms are isomorphism classes of spans of sets. We show that such structures are in correspondence with data
Groupoids
This paper gives some new results for the theory of quantum groupoids. First, the authors recall the relevant notions and results of the theory of Li-Rinehart algebras and bialgebras. Then, they
Frobenius objects in the category of relations
We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special
Introduction to the BV-BFV formalism
These notes give an introduction to the mathematical framework of the Batalin–Vilkovisky and Batalin–Fradkin–Vilkovisky formalisms.
...
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