Quantum idempotence, distributivity, and the Yang-Baxter equation

J. D. H. Smith

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 4, page 567-583
  • ISSN: 0010-2628

Abstract

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Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.

How to cite

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Smith, J. D. H.. "Quantum idempotence, distributivity, and the Yang-Baxter equation." Commentationes Mathematicae Universitatis Carolinae 57.4 (2016): 567-583. <http://eudml.org/doc/287558>.

@article{Smith2016,
abstract = {Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.},
author = {Smith, J. D. H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hopf algebra; quantum group; quasigroup; loop; quantum Yang-Baxter equation; distributive},
language = {eng},
number = {4},
pages = {567-583},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quantum idempotence, distributivity, and the Yang-Baxter equation},
url = {http://eudml.org/doc/287558},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Smith, J. D. H.
TI - Quantum idempotence, distributivity, and the Yang-Baxter equation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 4
SP - 567
EP - 583
AB - Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.
LA - eng
KW - Hopf algebra; quantum group; quasigroup; loop; quantum Yang-Baxter equation; distributive
UR - http://eudml.org/doc/287558
ER -

References

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