Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 97-121, 2017
On the quantum groups and semigroups of maps between noncommutative spaces
Maysam Maysami Sadr
Received July 18, 2015. First published February 24, 2017.
Abstract: We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are introduced: quantum group of gauge transformations, Pontryagin dual of a quantum group, and Galois-Hopf-algebra of an algebra extension.
Affiliations: Maysam Maysami Sadr, Department of Mathematics, Institute for Advanced Studies in Basic Sciences, No. 444, Prof. Yousef Sobouti Blvd., P. O. Box 45195-1159, Zanjan 45137-66731, Zanjan, Iran, e-mail: firstname.lastname@example.org