Results 11 to 20 of about 52 (51)

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.
Xue Chen
exaly   +3 more sources

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, Mohamed Wadia Mansouri   +1 more
doaj   +1 more source

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, Shengxiang Wang, Xiaohui Zhang   +2 more
doaj   +1 more source

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
doaj   +1 more source

Pointed Hopf algebras over nonabelian groups with nonsimple standard braidings

Proceedings of the London Mathematical Society, Volume 127, Issue 4, Page 1185-1245, October 2023., 2023
Abstract We construct finite‐dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We show conversely that every finite‐dimensional pointed Hopf algebra over a nonabelian group with nonsimple ...
Iván Angiono, Simon Lentner, Guillermo Sanmarco   +2 more
wiley   +1 more source

Gaudin algebras, RSK and Calogero–Moser cells in Type A

Proceedings of the London Mathematical Society, Volume 126, Issue 5, Page 1467-1495, May 2023., 2023
Abstract We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the n$n$‐fold tensor representation C[x1,…,xr]⊗n${\mathbb{C}}[x_1, \ldots , x_r]^{\otimes n}$ of the Lie algebra glr$\mathfrak {gl}_r$. We use the work of Halacheva–Kamnitzer–Rybnikov–Weekes to demonstrate that the Robinson–Schensted–Knuth ...
Adrien Brochier, Iain Gordon, Noah White
wiley   +1 more source

A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras

Bulletin of the London Mathematical Society, Volume 54, Issue 6, Page 2045-2065, December 2022., 2022
Abstract In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter (RB$\mathsf {RB}$) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L∞$L_\infty$‐algebra whose Maurer–Cartan elements are relative RB$\mathsf {RB}$ Lie algebras.
Yunhe Sheng
wiley   +1 more source

Integrable Defects and Bäcklund Transformations in Yang‐Baxter Models

Fortschritte der Physik, Volume 70, Issue 4, April 2022., 2022
Abstract We explore two distinct methods to introduce integrable defects in a family of integrable sigma‐models known as Yang‐Baxter models. The first method invokes a modified monodromy matrix encoding an integrable defect separating two integrable systems.
Saskia Demulder, Thomas Raml
wiley   +1 more source

Mirror symmetry for the Tate curve via tropical and log corals

Journal of the London Mathematical Society, Volume 105, Issue 1, Page 343-411, January 2022., 2022
Abstract We introduce tropical corals, balanced trees in a half‐space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve.
Hülya Argüz
wiley   +1 more source