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Central and invariant measures and applications
August 18, 2020 18:00–18:40, St. Petersburg, online
 


Polyhomomorphism of locally compact groups

Yu. A. Neretin
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Yu. A. Neretin


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Abstract: Let $G, H$ be locally compact groups equipped with fixed two-side invariant Haar measures. A polyhomomorphism $G\to H$ is a pair
– subgroup $\Gamma$ in the product $G\times H$,
– a Haar measure on $\Gamma$ whose projections to $G$ and $H$ are dominated by the Haar measures on $G$ and $H$.
The set of all polyhomomorphisms $G\to H$ is a compact set with respect to the Shabauty topology. Polyhomomorphisms form a category, i.e., there is a well-defined product of polyhomomorphisms $G_1\to G_2$ and $G_2\to G_3$. We discuss some properties of such objects and an example (polyendomorphisms of locally compact linear spaces over finite fields).

Language: English

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