Noncommutative Geometry and Representation Theory in Mathematical Physics

Fuchs, Jürgen; Mickelsson, Jouko; Rozenblioum, Grigori; Stolin, Alexander; Westerberg, Anders

doi:10.1090/conm/391

Cited by 7 publications

(1 citation statement)

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“…The antisymmetric r-matrices (6.10) are known to be associated with particular quantum Hopf-algebraic deformations of the D = 3 Poincaré algebra.r 3 ,r 2 andr 4 describe respectively the (twisted) time-, space-and lightlike κ-deformations (see [30] for the lightlike deformation and [31] for the twist), whiler 6 is a special combination of the twisted space-and lightlike κ-deformations;r 1 andr 5 are quasi-Jordanian deformations (cf. One can observe thatr 2 ,r 6 andr 7 are FR-compatible 14 (whenγ = 0), with α = √ 2γ in the formulae (6.7) and (6.9), whiler 3 is FR-compatible only if α = i √ 2γ, as it has recently been considered in [32] (it remains to be verified whether choosing α to be imaginary leads to a physically meaningful theory).…”

Section: D Gravity As Chern-simons Theorymentioning

confidence: 99%

Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits

Kowalski-Glikman

Lukierski

Trześniewski

2020

J. High Energ. Phys.

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Following the recently obtained complete classification of quantum-deformed $$ \mathfrak{o} $$ o (4), $$ \mathfrak{o} $$ o (1, 3) and $$ \mathfrak{o} $$ o (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail.

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Section: D Gravity As Chern-simons Theorymentioning

confidence: 99%

Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits

Kowalski-Glikman

Lukierski

Trześniewski

2020

J. High Energ. Phys.

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Monads of oplax actions are skew monoidales

Alcalá

2019

Journal of Pure and Applied Algebra

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Integrals for monoidal Hom-Hopf algebras and their applications

Chen

Wang

Zhang

2013

Journal of Mathematical Physics

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Integrals of monoidal Hom-Hopf algebras are introduced and the existence and uniqueness of integrals for finite-dimensional monoidal Hom-Hopf algebras are investigated first. Then integrals are applied to the Maschke type theorem for monoidal Hom-Hopf algebras controlling the semisimplicity and separability of monoidal Hom-Hopf algebras. Further, monoidal Hom-algebras are characterized with additional Frobenius property, and the question when finite-dimensional monoidal Hom-Hopf algebras are Frobenius is studied. As applications of integrals, the Maschke type theorem for Hom-smash product is given, and the Morita context in the Hom-category \documentclass[12pt]{minimal}\begin{document}$\widetilde{\mathcal {H}}(\mathcal {M}_k)$\end{document}H̃(Mk) is constructed.

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Noncommutative Geometry and Representation Theory in Mathematical Physics

Cited by 7 publications

References 0 publications

Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits

Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits

Monads of oplax actions are skew monoidales

Integrals for monoidal Hom-Hopf algebras and their applications

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