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4:00 pm Tuesday, November 4, 2008 Stulken Algebraic Geometry Seminar: Categorical algebraic geometry and associative algebrasby Travis Schedler (MIT/AIM) in HB 227- Affine algebraic geometry is based on the category of commutative algebras, i.e., monoids in the category of vector spaces. On the other hand, it is often important to enhance vector spaces, and study, e.g., super or dg algebras, or commutative Lie monoids. Call this ``categorical algebraic geometry.''
I will define an embedding of associative (noncommutative) algebras into categorical algebraic geometry. Precisely, I embed every associative algebra A into a commutative algebra, "F(A)," in the category of ``wheelspaces.'' This allows me to generalize Grothendieck's construction of differential operators to F(A). Following Kontsevich's philosophy, these map to differential operators on representation varieties of A. This generalizes so-called "noncommutative symplectic/Poisson geometry" of Van den Bergh, Crawley-Boevey, Etingof, and Ginzburg. This work is joint with V. Ginzburg. Submitted by hassett@math.rice.edu |