Structure of some compact quantum semigroups

Aukhadiev M. A.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 2.

Abstract:
We show that the main results of multuplicative unitary theory do not hold for compact quantum semigroups and give examples. We suggest a new method to provide compact quantum semigroup structure by the use of pentagon equation, which gives a generalization of multiplicative unitary theory.

Keywords: quantum semigroup, quantum group, Haar functional, Toeplitz algebra, multiplicative unitary, pentagon equation

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