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New Universal Deformation Formulas for deformation quantization
Murray Gerstenhaber
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 infin…
Deformations associated to rigid algebras
Murray Gerstenhaber, Anthony Giaquinto
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional…
On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra
Murray Gerstenhaber, Anthony Giaquinto
Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare cha…
Graphs, Frobenius functionals, and the classical Yang-Baxter equation
Murray Gerstenhaber, Anthony Giaquinto
A Lie algebra is Frobenius if it admits a linear functional F such that the Kirillov form F([x,y]) is non-degenerate. If g is the m-th maximal parabolic subalgebra P(n,m) of sl(n)…
A selection principle in deformation quantization
Murray Gerstenhaber
Deformation quantization produces families of mathematically equivalent quantization procedures from which one must select the physically meaningful ones. As a selection principle…
The Donald-Flanigan problem for finite reflection groups
Murray Gerstenhaber, Anthony Giaquinto, Mary E. Schaps
The Donald--Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral group…