Operator approach to quantization of semigroups

M. A. Aukhadiev   ; S. A. Grigoryan   ; E. V. Lipacheva

Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 319-342

Résumé

The paper is devoted to the construction of compact quantum semigroups from semigroup $C^*$-algebras generated by the ‘deformation’ of algebras of continuous functions on compact Abelian groups. The dual space of such a $C^*$-algebra is endowed with the structure of a Banach *-algebra containing the algebra of measures on a compact group. We construct a weak Hopf *-algebra that is dense in such a compact quantum semigroup. We show that there exists an injective functor from the constructed category of compact quantum semigroups into the category of Abelian semigroups. Bibliography: 25 titles.

Détail

Keywords: $C^*$-algebra, compact quantum semigroup, Haar functional, Toeplitz algebra, isometric representation.

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