Covariantization of quantized calculi over quantum groups
Seyed Ebrahim Akrami; Shervin Farzi
Mathematica Bohemica (2020)
- Volume: 145, Issue: 4, page 415-433
- ISSN: 0862-7959
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topAkrami, Seyed Ebrahim, and Farzi, Shervin. "Covariantization of quantized calculi over quantum groups." Mathematica Bohemica 145.4 (2020): 415-433. <http://eudml.org/doc/297073>.
@article{Akrami2020,
abstract = {We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$. We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra $A^\circ $. We apply this method to the Dirac operator for the quantum $\rm SL(2)$ given by S. Majid. We find that the differential calculus obtained by our method is the standard bicovariant 4D-calculus. We also apply this method to the Dirac operator for the quantum $\rm SL(2)$ given by P. N. Bibikov and P. P. Kulish and show that the resulted differential calculus is $8$-dimensional.},
author = {Akrami, Seyed Ebrahim, Farzi, Shervin},
journal = {Mathematica Bohemica},
keywords = {Hopf algebra; quantum group; covariant first order differential calculus; quantized calculus; Dirac operator},
language = {eng},
number = {4},
pages = {415-433},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Covariantization of quantized calculi over quantum groups},
url = {http://eudml.org/doc/297073},
volume = {145},
year = {2020},
}
TY - JOUR
AU - Akrami, Seyed Ebrahim
AU - Farzi, Shervin
TI - Covariantization of quantized calculi over quantum groups
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 4
SP - 415
EP - 433
AB - We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$. We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra $A^\circ $. We apply this method to the Dirac operator for the quantum $\rm SL(2)$ given by S. Majid. We find that the differential calculus obtained by our method is the standard bicovariant 4D-calculus. We also apply this method to the Dirac operator for the quantum $\rm SL(2)$ given by P. N. Bibikov and P. P. Kulish and show that the resulted differential calculus is $8$-dimensional.
LA - eng
KW - Hopf algebra; quantum group; covariant first order differential calculus; quantized calculus; Dirac operator
UR - http://eudml.org/doc/297073
ER -
References
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