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 Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 10, Pages 43–54 (Mi ivm9404)

On a class of graded ideals of semigroup $C^*$-algebras

E. V. Lipacheva

Kazan State Power Engineering University, 51 Krasnosel’skaya str., Kazan, 420066 Russia

Abstract: We present general results about graded $C^*$-algebras and continue the previously initiated research of the $C^*$-algebra generated by the left regular representation of an Abelian semigroup. We study the invariant ideals of this $C^*$-algebra invariant with respect to the representation of a compact group $G$ in the automorphism group of this algebra. We prove that the invariance of the ideal is equivalent to the fact that this ideal is graded $C^*$-algebra, that there is a maximum of all invariant ideals, and it is the commutator ideal. Separately we study a class of graded primitive ideals generated by a single projector.

Keywords: $C^*$-algebra, graded $C^*$-algebra, semigroup, left regular representation, invariant subspace, representation in the automorphism group, invariant ideal, commutator ideal.

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UDC: 512.579

Citation: E. V. Lipacheva, “On a class of graded ideals of semigroup $C^*$-algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 10, 43–54

Citation in format AMSBIB
\Bibitem{Lip18} \by E.~V.~Lipacheva \paper On a class of graded ideals of semigroup $C^*$-algebras \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2018 \issue 10 \pages 43--54 \mathnet{http://mi.mathnet.ru/ivm9404}