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Deformation Theory Seminar

Wednesday, March 14, 2018 - 2:00pm

Murray Gerstenhaber

U Penn


University of Pennsylvania



Universal Deformation Formulas (UDFs) for the deformation of associative algebras play a key role in deformation quantization. Here we present examples for certain classes of infinitesimals. A basic separable 2- cocycle F of an associative algebra A is one for which there exist commuting derivations D_1,...,D_n of A such that F = \sum_{ij}a_{ij}D_i \smile D_j$, where the $a_{ij}$ are central elements of A. When A is defined over the rationals, there is a natural definition of the exponential of such a cocycle. With this,  exp F defines a formal one-parameter family of deformations of A. The rational quantization of smooth functions on a smooth manifold using a bivector field as an infinitesimal deformation is a special case.