M. A. Semenov-Tian-Shansky, “Poisson–Lie groups. The quantum duality principle and the twisted quantum double”, TMF, 93:2 (1992), 302–329; Theoret. and Math. Phys., 93:2 (1992), 1292

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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 93, Number 2, Pages 302–329 (Mi tmf1530)

This article is cited in 56 scientific papers (total in 56 papers)

Poisson–Lie groups. The quantum duality principle and the twisted quantum double

M. A. Semenov-Tian-Shansky

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full-text PDF (2373 kB) Citations (56)

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Abstract: The quantum duality principle relates the quantum groups that arise on the quantization of Poisson–Lie dual groups and generalizes Fourier duality. Also considered are the theory of the Heisenberg double, which replaces the cotangent bundle for quantum groups, and its deformations (the twisted double).

Received: 18.06.1992

English version:
Theoretical and Mathematical Physics, 1992, Volume 93, Issue 2, Pages 1292–1307
DOI: https://doi.org/10.1007/BF01083527

Bibliographic databases:

Language: Russian

Citation: M. A. Semenov-Tian-Shansky, “Poisson–Lie groups. The quantum duality principle and the twisted quantum double”, TMF, 93:2 (1992), 302–329; Theoret. and Math. Phys., 93:2 (1992), 1292–1307

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1530

https://www.mathnet.ru/eng/tmf/v93/i2/p302

This publication is cited in the following 56 articles:

Valentin Bonzom, Maïté Dupuis, Florian Girelli, Qiaoyin Pan, “Local observables in SUq(2) lattice gauge theory”, Phys. Rev. D, 107:2 (2023)
Hank Chen, Florian Girelli, “Categorified Drinfel'd double and BF theory: 2-groups in 4D”, Phys. Rev. D, 106:10 (2022)
Florian Girelli, Panagiotis Tsimiklis, “Discretization of 4D Poincaré BF theory: From groups to 2-groups”, Phys. Rev. D, 106:4 (2022)
Angel Ballesteros, Ivan Gutierrez-Sagredo, Flavio Mercati, “Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces”, J. Phys. A: Math. Theor., 54:31 (2021), 315203
Alexander Spies, “Poisson-geometric Analogues of Kitaev Models”, Commun. Math. Phys., 383:1 (2021), 345
Catherine Meusburger, “Poisson–Lie Groups and Gauge Theory”, Symmetry, 13:8 (2021), 1324
Doliwa A. Kashaev R.M., “Non-Commutative Birational Maps Satisfying Zamolodchikov Equation, and Desargues Lattices”, J. Math. Phys., 61:9 (2020), 092704
Francesco Bascone, Franco Pezzella, Patrizia Vitale, “Poisson-Lie T-duality of WZW model via current algebra deformation”, J. High Energ. Phys., 2020:9 (2020)
Vincenzo E. Marotta, Franco Pezzella, Patrizia Vitale, “T-dualities and Doubled Geometry of the Principal Chiral Model”, J. High Energ. Phys., 2019:11 (2019)
Gleb Arutyunov, Rob Klabbers, Enrico Olivucci, “Quantum trace formulae for the integrals of the hyperbolic Ruijsenaars-Schneider model”, J. High Energ. Phys., 2019:5 (2019)
Mercati F., Sergola M., “Physical Constraints on Quantum Deformations of Spacetime Symmetries”, Nucl. Phys. B, 933 (2018), 320–339
Ángel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernández-Saiz, Francisco J Herranz, Javier de Lucas, “Poisson–Hopf algebra deformations of Lie–Hamilton systems”, J. Phys. A: Math. Theor., 51:6 (2018), 065202
A. Ballesteros, G. Gubitosi, I. Gutierrez-Sagredo, F. J. Herranz, “Curved momentum spaces from quantum (anti–)de Sitter groups in ( 3+1 ) dimensions”, Phys. Rev. D, 97:10 (2018)
Vincenzo E. Marotta, Franco Pezzella, Patrizia Vitale, “Doubling, T-Duality and Generalized Geometry: a simple model”, J. High Energ. Phys., 2018:8 (2018)
Giacomo Rosati, “κ –de Sitter and κ -Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant”, Phys. Rev. D, 96:6 (2017)
Gus Schrader, Alexander Shapiro, “Quantum groups, quantum tori, and the Grothendieck–Springer resolution”, Advances in Mathematics, 321 (2017), 431
Gus Schrader, Alexander Shapiro, “Dual pairs of quantum moment maps and doubles of Hopf algebras”, Journal of Algebra, 492 (2017), 74
Á. Ballesteros, G. Gubitosi, I. Gutiérrez-Sagredo, F.J. Herranz, “Curved momentum spaces from quantum groups with cosmological constant”, Physics Letters B, 773 (2017), 47
Ángel Ballesteros, Francisco J. Herranz, Fabio Musso, Pedro Naranjo, “The κ-(A)dS quantum algebra in (3 + 1) dimensions”, Physics Letters B, 766 (2017), 205
Pavel Pyatov, “On the construction of unitary quantum group differential calculus”, J. Phys. A: Math. Theor., 49:41 (2016), 415202

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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