12 citations · 13 across the 7 of their papers we have counts for
8 papers
Groupoids viewed as inverse semigroups
Marat Aukhadiev
A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fa…
An inverse semigroup approach to the C*-algebras and crossed products of cancellative semigroups
Marat Aukhadiev
We give a new definition of the semigroup C*-algebra of a left cancellative semigroup, which resolves problems of the construction by X. Li. Namely, the new construction is functor…
Quantum semigroups generated by locally compact semigroups
Marat A. Aukhadiev, Yulia N. Kuznetsova
Let be a subsemigroup of a second countable locally compact group , such that . We consider the -algebra generated by the operators of translation…
A crossed product of the CAR algebra in the Cuntz algebra
Marat Aukhadiev, Alexander Nikitin, Airat Sitdikov
In this paper we show that the Cuntz algebra can be represented as a C*-crossed product by endomorphism of the canonical anticommutation relations (CAR) algebra, generated by the s…
Semigroup Operator Algebras and Quantum Semigroups
Marat Aukhadiev, Suren Grigoryan, Ekaterina Lipacheva
A detailed study of the semigroup -algebra is presented. This -algebra appears as a "deformation" of the continuous functions algebra on a compact abelian group. Co…
Isometric Representations of Totally Ordered Semigroups
M. A. Aukhadiev, V. H. Tepoyan
Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S ar…