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Noncommutative discriminants and Poisson primes

Banff International Research Station for Mathematical Innovation and Discovery

Discriminants play a key role in the study of PI algebras (PIAs): orders in central simple algebras, Azumaya loci of PIAs, the isomorphism and automorphism problems for PIAs. Previously, they were computed for very few PI algebras. We will present a general method for computing discriminants of PIAs which is applicable to algebras obtained by specialization from families, such as quantum algebras at roots of unity. It relies on a connection with Poisson geometry. From a different perspective the technique builds a bridge to the theory of discriminants of number fields, where factorizations into primes are replaced by factorizations into Poisson primes. This is a joint work with Jesse Levitt, Bach Nguyen and Kurt Trampel.

Mathematics; Associative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: Louisiana State University

2017-03-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60897

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/