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On a Class of Graded Ideals of Semigroup C*-Algebras

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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.

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Authors and Affiliations

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

    E. V. Lipacheva

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  1. E. V. Lipacheva
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Correspondence to E. V. Lipacheva.

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Original Russian Text © E.V. Lipacheva, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 10, pp. 43–54.

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Lipacheva, E.V. On a Class of Graded Ideals of Semigroup C*-Algebras. Russ Math. 62, 37–46 (2018). https://doi.org/10.3103/S1066369X18100055

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