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.

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

Meeting ID: 878 5613 2062