Deformation and Hochschild Cohomology of Coisotropic Algebras

TL;DR

This paper develops a formal deformation theory for coisotropic algebras, showing that their deformations are controlled by coisotropic differential graded Lie algebras and that deformation processes commute with reduction.

Contribution

It introduces a deformation functor for coisotropic algebras, proves its compatibility with reduction, and explores obstructions and geometric examples.

Findings

Deformations governed by coisotropic DGLAs.

Deformation functor commutes with reduction.

Identified obstructions to deformation existence and uniqueness.

Abstract

Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.