# Coisotropic Triples, Reduction and Classical Limit

### Marvin Dippell

Julius Maximilian University of Würzburg, Department of Mathematics, Chair of Mathematics X (Mathematical Physics), Emil-Fischer-Straße 31, 97074 Würzburg, Germany### Chiara Esposito

Dipartimento di Matematica, Università degli Studi di Salerno, via Giovanni Paolo II, 123 84084 Fisciano (SA), Italy### Stefan Waldmann

Julius Maximilian University of Würzburg, Department of Mathematics, Chair of Mathematics X (Mathematical Physics), Emil-Fischer-Straße 31, 97074 Würzburg, Germany

## Abstract

Coisotropic reduction from Poisson geometry and deformation quantization is cast into a general and unifying algebraic framework: we introduce the notion of coisotropic triples of algebras for which a reduction can be defined. This allows to construct also a notion of bimodules for such triples leading to bicategories of bimodules for which we have a reduction functor as well. Morita equivalence of coisotropic triples of algebras is defined as isomorphism in the ambient bicategory and characterized explicitly. Finally, we investigate the classical limit of coisotropic triples of algebras and their bimodules and show that classical limit commutes with reduction in the bicategory sense.

## Cite this article

Marvin Dippell, Chiara Esposito, Stefan Waldmann, Coisotropic Triples, Reduction and Classical Limit. Doc. Math. 24 (2019), pp. 1811–1853

DOI 10.4171/DM/716