On the quantum groups and semigroups of maps between noncommutative spaces

Maysam Maysami Sadr

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 1, page 97-121
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Sadr, Maysam Maysami. "On the quantum groups and semigroups of maps between noncommutative spaces." Czechoslovak Mathematical Journal 67.1 (2017): 97-121. <http://eudml.org/doc/287902>.

@article{Sadr2017,
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.},
author = {Sadr, Maysam Maysami},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hopf-algebra; bialgebra; quantum group; noncommutative geometry; quantum semigroup structure},
language = {eng},
number = {1},
pages = {97-121},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the quantum groups and semigroups of maps between noncommutative spaces},
url = {http://eudml.org/doc/287902},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Sadr, Maysam Maysami
TI - On the quantum groups and semigroups of maps between noncommutative spaces
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 97
EP - 121
AB - 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.
LA - eng
KW - Hopf-algebra; bialgebra; quantum group; noncommutative geometry; quantum semigroup structure
UR - http://eudml.org/doc/287902
ER -

References

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