Speaker:  Eugene Rogozinnikov (Max-Planck-Institut für Mathematik in den Wissenschaften (MPI MiS), Leipzig, Germany)

Date and time:  10.04.2024, 17:00 (GMT +03:00)

Title: Hermitian Lie groups as symplectic groups over noncommutative algebras

Abstract: In my talk (based on a joint work with D. Alessandrini, A. Berenstein, V. Retakh and A. Wienhard), I introduce the symplectic group $Sp_2(A,\sigma)$ over a noncommutative algebra $A$ with an anti-involution $\sigma$ and show that many Lie groups can be seen in this way. Of particular interest will be the classical Hermitian Lie groups such as $Sp(2n,R)$, $U(n,n)$ and their complexifications. For these groups, I realize their symmetric space in terms of $Sp_2(A,\sigma)$ thus generalizing several famous models of the hyperbolic plane and the three-dimensional hyperbolic space. Our construction has a flavor of noncommutative projective line over the complexification of $A$ which is always a compact symmetric space when $A$ Hermitian and semisimple or its complexification. We expect it to hold for any semisimple $A$. This, in turn, would imply that $Sp_2(A,\sigma)$ is reductive when $A$ is semisimple.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com