Maximal Ideal Spaces of Invariant Function Algebras on Compact Groups

Maximal Ideal Spaces of Invariant Function Algebras on Compact Groups Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2023, Volume: 33, Number: 2, Pages: 107–139 Pages count : 33 DOI: 10.1134/S1055134423020025

Tags

invariant function algebra, maximal ideal space, complex Lie semigroup.

Authors

Gichev V.M. ¹

Affiliations

1	Sobolev Institute of Mathematics, Omsk Division, Omsk, 644099 Russia

Let G be a compact group and A be a closed subalgebra of C(G) which is invariant under the left and right shifts in G. We consider maximal ideal spaces (spectra) MA of these algebras. They can be defined as closed sub-bialgebras of C(G). There is a natural semigroup structure in MA that admits an involutive anti-automorphism and a polar decomposition. If MA = G then MA has a nontrivial analytic structure. If G is a Lie group then every idempotent in MA is the identity element of a complex Lie semigroup embedded to MA. The semigroup MA admits an analogue of Cartan’s decomposition KAK, namely, MA = GTG , where T is an abelian semigroup that is a hull of the maximal torus T .

Gichev V.M.
Maximal Ideal Spaces of Invariant Function Algebras on Compact Groups
Siberian Advances in Mathematics. 2023. V.33. N2. P.107–139. DOI: 10.1134/S1055134423020025 Scopus РИНЦ OpenAlex

Гичев В.М.
Пространства максимальных идеалов инвариантных алгебр функций на компактных группах
Математические труды. 2022. Т.25. №2. С.31-87. DOI: 10.33048/mattrudy.2022.25.202 РИНЦ

Submitted:	Oct 3, 2022
Accepted:	Nov 2, 2022
Published print:	May 25, 2023
Published online:	May 25, 2023

Scopus:	2-s2.0-85160272520
Elibrary:	61528013
OpenAlex:	W1814987579

DB	Citing
OpenAlex	3