Operator approach to quantization of semigroups

Journal Article · Mon Mar 31 00:00:00 EDT 2014 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2014V205N03ABEH004378· OSTI ID:22365577

Aukhadiev, M A; Grigoryan, S A; Lipacheva, E V ^[1]

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1. Kazan State Power Engineering University, Kazan (Russian Federation)

The paper is devoted to the construction of compact quantum semigroups from semigroup C{sup ∗}-algebras generated by the 'deformation' of algebras of continuous functions on compact Abelian groups. The dual space of such a C{sup ∗}-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.

• OSTI ID: 22365577
• Journal Information: Sbornik. Mathematics, Vol. 205, Issue 3; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGEBRA
DEFORMATION
FUNCTIONS
GROUP THEORY
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
QUANTIZATION