Algebra Seminar[ Edit ]
Moderator: Danny Neftin
By Quantum Matrix algebras one usually means the algebras defined via braidings,i.e. solutions to the Quantum Yang-Baxter equation. I plan to discuss the problemof classification of braidings. Also, I plan to introduce some Quantum Matrixalgebras and exhibit their properties. In particular, I plan to definequantum analogs of basic symmetric polynomials (elementary, full, Schur...)and to present a quantum version of the Cayley-Hamilton identity.The talk is supposed to be introductory.
Under the assumption of the GRH(Generalized Riemann Hypothesis), we show that there is a real quadratic field K such that the étale fundamental group of the spectrum of the ring of integers of K is isomorphic to A5. To the best of the author's knowledge, this is the first example of a nonabelian simple étale fundamental group in the literature under the assumption of the GRH. (The talk will be basic and tha above notions will be defined).