Geodesic
Operator approach to quantization of semigroups
Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 319-342

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: $C^*$-algebra, compact quantum semigroup, Haar functional, Toeplitz algebra, isometric representation. 
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M. A. Aukhadiev; S. A. Grigoryan; E. V. Lipacheva. Operator approach to quantization of semigroups. Sbornik. Mathematics, Tome 205 (2014) no. 3, pp. 319-342. http://geodesic.mathdoc.fr/item/SM_2014_205_3_a1/