Results 1 to 10 of about 83 (77)
LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS
Ural Mathematical Journal, 2021 The paper deals with linearization problem of Poisson-Lie structures on the \((1+1)\) Poincaré and \(2D\) Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-
Bousselham Ganbouri +1 more
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3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
Mathematics, 2022 In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-Hom–Lie algebras.
Shuangjian Guo +2 more
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Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra
Mathematics, 2023 The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations.
Yihong Su, Xue Chen
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Classical Lie bialgebras for AdS/CFT integrability by contraction and reduction
SciPost Physics, 2023 Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra.
Niklas Beisert, Egor Im
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Physical constraints on quantum deformations of spacetime symmetries
Nuclear Physics B, 2018 In this work we study the deformations into Lie bialgebras of the three relativistic Lie algebras: de Sitter, Anti-de Sitter and Poincaré, which describe the symmetries of the three maximally symmetric spacetimes. These algebras represent the centerpiece
Flavio Mercati, Matteo Sergola
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The κ-(A)dS quantum algebra in (3+1) dimensions
Physics Letters B, 2017 The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group.
Ángel Ballesteros +3 more
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Quantization of the Rank Two Heisenberg–Virasoro Algebra
AxiomsQuantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras.
Xue Chen
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Atiyah classes of three-dimensional Lie bialgebras over Z_3
四川大学学报. 自然科学版, 2019 Based on the theory of Lie algebra cohomology and the definition of the Atiyah class of a Lie bialgebra, Atiyah classes of all three-dimensional Lie bialgebras over Z_3 are calculated.
SHEN Dan-Dan
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Cumulants, free cumulants and half-shuffles. [PDF]
Proc Math Phys Eng Sci, 2015 Ebrahimi-Fard K, Patras F.
europepmc +1 more source
Cremmer-Gervais cluster structure on SLn. [PDF]
Proc Natl Acad Sci U S A, 2014 Gekhtman M, Shapiro M, Vainshtein A.
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