Geodesic
On the quantum groups and semigroups of maps between noncommutative spaces
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 97-121.

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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.
DOI : 10.21136/CMJ.2017.0393-15
Classification : 16T05, 16T10, 16T20, 58B34
Keywords: Hopf-algebra; bialgebra; quantum group; noncommutative geometry 
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Sadr, Maysam Maysami. On the quantum groups and semigroups of maps between noncommutative spaces. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 97-121. doi : 10.21136/CMJ.2017.0393-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0393-15/

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