Geodesic
On a class of graded ideals of semigroup $C^*$-algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 43-54

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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. 
@article{IVM_2018_10_a4,
     author = {E. V. Lipacheva},
     title = {On a class of graded ideals of semigroup $C^*$-algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {43--54},
     publisher = {mathdoc},
     number = {10},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_10_a4/}
}
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E. V. Lipacheva. On a class of graded ideals of semigroup $C^*$-algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 43-54. http://geodesic.mathdoc.fr/item/IVM_2018_10_a4/