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Addition theorems and related geometric problems of group representation theory

Ekaterina Shulman (2013)

Banach Center Publications

The Levi-Civita functional equation f ( g h ) = k = 1 n u k ( g ) v k ( h ) (g,h ∈ G), for scalar functions on a topological semigroup G, has as the solutions the functions which have finite-dimensional orbits in the right regular representation of G, that is the matrix elements of G. In considerations of some extensions of the L-C equation one encounters with other geometric problems, for example: 1) which vectors x of the space X of a representation g T g have orbits O(x) that are “close” to a fixed finite-dimensional subspace? 2) for...

Almost maximal topologies on groups

Yevhen Zelenyuk (2016)

Fundamenta Mathematicae

Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...

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