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Title: Operator approach to quantization of semigroups

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.
Authors:
; ;  [1]
  1. Kazan State Power Engineering University, Kazan (Russian Federation)
Publication Date:
OSTI Identifier:
22365577
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 3; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; DEFORMATION; FUNCTIONS; GROUP THEORY; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; QUANTIZATION