# Topological and mixing properties for algebraic groups over local fields in characteristic zero

Seminar

Speaker

Elyasheev Leibtag (Weizmann Institute of Science)

Date

05/06/2024 - 11:30 - 10:30Add to Calendar

`2024-06-05 10:30:30``2024-06-05 11:30:00``Topological and mixing properties for algebraic groups over local fields in characteristic zero``We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite- dimensional and mixing representations, and the matrix coefficients are dense within the algebra of weakly almost periodic functions over the group. In our proof, we employ methods from semi-group theory. We establish that these groups are compactification-centric, meaning sG = Gs for any element s in the weakly almost periodic compactification of the group G. ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062``Third floor seminar room and Zoom``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room and Zoom

Abstract

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent:

Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite- dimensional and mixing representations, and the matrix coefficients are dense within the algebra of weakly almost periodic functions over the group.

In our proof, we employ methods from semi-group theory. We establish that these groups are *compactification-centric*, meaning *sG *= *Gs *for any element *s *in the weakly almost periodic compactification of the group *G*.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 29/05/2024