Poisson and Hochschild cohomology and the semiclassical limit

2013/04/22 by Matthew Towers, Towers, Matthew
Mathematics · #16E40 #17B63 #20G42 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:16E40 #msc:17B63 #msc:20G42

paper · pdf · doi:10.48550/arxiv.1304.6003

Comments to [email protected] welcome

arxiv created 2013/05/06 · arxiv updated 2013/05/07

Abstract

Let B be a quantum algebra possessing a semiclassical limit A. We show that under certain hypotheses B^e can be thought of as a deformation of the Poisson enveloping algebra of A, and we give a criterion for the Hochschild cohomology of B to be a deformation of the Poisson cohomology of A in the case that B is Koszul. We verify that condition for the algebra of 2× 2 quantum matrices and calculate its Hochschild cohomology and the Poisson cohomology of its semiclassical limit.

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