Braided coproduct, antipode and adjoint action for U q ( s l 2 )

Pavle Pandžić; Petr Somberg

Archivum Mathematicum (2024)

  • Volume: 060, Issue: 5, page 365-376
  • ISSN: 0044-8753

Abstract

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Motivated by our attempts to construct an analogue of the Dirac operator in the setting of U q ( 𝔰𝔩 n ) , we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra U q ( 𝔰𝔩 2 ) . The braided adjoint action is seen to coincide with the ordinary quantum adjoint action, which also follows from the general results of S. Majid.

How to cite

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Pandžić, Pavle, and Somberg, Petr. "Braided coproduct, antipode and adjoint action for $U_q(sl_2)$." Archivum Mathematicum 060.5 (2024): 365-376. <http://eudml.org/doc/299617>.

@article{Pandžić2024,
abstract = {Motivated by our attempts to construct an analogue of the Dirac operator in the setting of $U_q(\mathfrak \{sl\}_n)$, we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra $U_q(\mathfrak \{sl\}_2)$. The braided adjoint action is seen to coincide with the ordinary quantum adjoint action, which also follows from the general results of S. Majid.},
author = {Pandžić, Pavle, Somberg, Petr},
journal = {Archivum Mathematicum},
keywords = {quantum group; quantum $\mathfrak \{sl\}_2$; quantum adjoint action; tensor categories; braided tensor product; braided adjoint action},
language = {eng},
number = {5},
pages = {365-376},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Braided coproduct, antipode and adjoint action for $U_q(sl_2)$},
url = {http://eudml.org/doc/299617},
volume = {060},
year = {2024},
}

TY - JOUR
AU - Pandžić, Pavle
AU - Somberg, Petr
TI - Braided coproduct, antipode and adjoint action for $U_q(sl_2)$
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 060
IS - 5
SP - 365
EP - 376
AB - Motivated by our attempts to construct an analogue of the Dirac operator in the setting of $U_q(\mathfrak {sl}_n)$, we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra $U_q(\mathfrak {sl}_2)$. The braided adjoint action is seen to coincide with the ordinary quantum adjoint action, which also follows from the general results of S. Majid.
LA - eng
KW - quantum group; quantum $\mathfrak {sl}_2$; quantum adjoint action; tensor categories; braided tensor product; braided adjoint action
UR - http://eudml.org/doc/299617
ER -

References

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  9. Majid, S., 10.1088/1751-8121/ac631f, J. Phys. A: Math. Theor. 55 (2022), 34 pp., paper No. 254007. (2022) MR4438638DOI10.1088/1751-8121/ac631f
  10. Pandžić, P., Somberg, P., Dirac operator for the quantum group U q ( 𝔰𝔩 3 ) , in preparation. 
  11. Pandžić, P., Somberg, P., Dirac operator and its cohomology for the quantum group U q ( 𝔰𝔩 2 ) , J. Math. Phys. 58 (4) (2017), 13 pp., Paper No. 041702. (2017) MR3632540
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  13. Vogan, D., Dirac operators and unitary representations, 3 talks at MIT Lie groups seminar, Fall 1997. 

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