Arithmetic Study Group: Deformations of crossed product algebras and orbifolds
17 November 2015 14:00 in CM219
Given a group G acting on a space X, one can construct the crossed product algebra G \ltimes C[X] of G with the algebra of functions on X. This generally noncommutative algebra can be seen as a replacement for the algebra of functions on the quotient X/G, which may be badly behaved.
I will speak about deformations of these algebras - both formal deformations (in the sense of Gerstenhaber) and strict deformations (in the sense of Rieffel). I will explain a general construction for producing such deformations and describe some examples. I will then explain how certain geometric and algebraic properties of these deformations are related to certain questions in representation theory, and to the geometry of the original action of G on X.
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