We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a bicovariant bimodule and its cocycle deformations are in one to one correspondence.
Bhowmick, Jyotishman 1 ; Mukhopadhyay, Sugato 1
CC-BY 4.0
@article{AMBP_2020__27_2_159_0,
author = {Bhowmick, Jyotishman and Mukhopadhyay, Sugato},
title = {Pseudo-Riemannian metrics on bicovariant bimodules},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {159--180},
year = {2020},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {27},
number = {2},
doi = {10.5802/ambp.394},
language = {en},
url = {https://www.numdam.org/articles/10.5802/ambp.394/}
}
TY - JOUR AU - Bhowmick, Jyotishman AU - Mukhopadhyay, Sugato TI - Pseudo-Riemannian metrics on bicovariant bimodules JO - Annales mathématiques Blaise Pascal PY - 2020 SP - 159 EP - 180 VL - 27 IS - 2 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://www.numdam.org/articles/10.5802/ambp.394/ DO - 10.5802/ambp.394 LA - en ID - AMBP_2020__27_2_159_0 ER -
%0 Journal Article %A Bhowmick, Jyotishman %A Mukhopadhyay, Sugato %T Pseudo-Riemannian metrics on bicovariant bimodules %J Annales mathématiques Blaise Pascal %D 2020 %P 159-180 %V 27 %N 2 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://www.numdam.org/articles/10.5802/ambp.394/ %R 10.5802/ambp.394 %G en %F AMBP_2020__27_2_159_0
Bhowmick, Jyotishman; Mukhopadhyay, Sugato. Pseudo-Riemannian metrics on bicovariant bimodules. Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 2, pp. 159-180. doi: 10.5802/ambp.394
[1] Hopf algebras, Cambridge Tracts in Mathematics, 74, Cambridge University Press, 1980, xii+284 pages (Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka) | MR | Zbl
[2] Covariant connections on bicovariant differential calculus, J. Algebra, Volume 563 (2020), pp. 198-250 | Zbl | MR | DOI
[3] Hopf–Galois objects and cogroupoids, Rev. Unión Mat. Argent., Volume 55 (2014) no. 2, pp. 11-69 | Zbl | MR
[4] Braided bialgebras and quadratic bialgebras, Commun. Algebra, Volume 21 (1993) no. 5, pp. 1731-1749 | Zbl | MR | DOI
[5] Tensor categories, Mathematical Surveys and Monographs, 205, American Mathematical Society, 2015, xvi+343 pages | Zbl | MR | DOI
[6] Hodge and Laplace-Beltrami operators for bicovariant differential calculi on quantum groups, Compos. Math., Volume 123 (2000) no. 3, pp. 329-354 | Zbl | MR | DOI
[7] Spin geometry on quantum groups via covariant differential calculi, Adv. Math., Volume 175 (2003) no. 2, pp. 197-242 | Zbl | MR | DOI
[8] Levi-Civita connections on the quantum groups , and , Commun. Math. Phys., Volume 185 (1997) no. 1, pp. 177-196 | Zbl | MR | DOI
[9] Quantum groups, Graduate Texts in Mathematics, 155, Springer, 1995, xii+531 pages | Zbl | MR | DOI
[10] Noncommutative Riemannian and spin geometry of the standard -sphere, Commun. Math. Phys., Volume 256 (2005) no. 2, pp. 255-285 | MR | DOI
[11] Quantum Riemannian geometry, Springer, 2019 | Zbl | DOI
[12] Twisting of quantum differentials and the Planck scale Hopf algebra, Commun. Math. Phys., Volume 205 (1999) no. 3, pp. 617-655 | Zbl | MR | DOI
[13] Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, 82, American Mathematical Society, 1993, xiv+238 pages | Zbl | MR | DOI
[14] Hopf modules and Yetter-Drinfel’d modules, J. Algebra, Volume 169 (1994) no. 3, pp. 874-890 | Zbl | MR | DOI
[15] Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., 1969, vii+336 pages | Zbl | MR
[16] Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys., Volume 122 (1989) no. 1, pp. 125-170 | Zbl | DOI | MR
[17] Quantum groups and representations of monoidal categories, Math. Proc. Camb. Philos. Soc., Volume 108 (1990) no. 2, pp. 261-290 | Zbl | MR | DOI
Cité par Sources :
