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Register a new userHochschild Cohomology and Deformations of Clifford-Weyl Algebras
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We give a complete study of the Clifford-Weyl algebra ${mathcal C}(n,2k)$ from Bose-Fermi statistics, including Hochschild cohomology (with coefficients in itself). We show that ${mathcal C}(n,2k)$ is rigid when $n$ is even or when $k eq 1$. We find all non-trivial deformations of ${mathcal C}(2n+1,2)$ and study their representations.
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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.
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