Results 21 to 30 of about 1,412 (138)

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

On Lie induction and the exceptional series [PDF]

, 2005
Lie bialgebras occur as the principal objects in the infinitesimalization of the theory of quantum groups — the semi-classical theory. Their relationship with the quantum theory has made available some new tools that we can apply to classical questions ...
Grabowski, Jan
core   +5 more sources

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

Averaging antisymmetric infinitesimal bialgebra and perm bialgebras

We establish a bialgebra theory for averaging algebras, called averaging antisymmetric infinitesimal bialgebras by generalizing the study of antisymmetric infinitesimal bialgebras to the context of averaging algebras. They are characterized by double constructions of averaging Frobenius algebras as well as matched pairs of averaging algebras ...
Hou, Bo, Cui, Zhanpeng
openaire   +3 more sources

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

On Quadri-Bialgebras

, 2022
We introduce the notion of a quadri-bialgebra, which gives a bialgebra theory for the quadri-algebra introduced by Aguiar and Loday. We show that a quadri-bialgebra is equivalent to a Manin triple of dendriform algebras associated to a nondegenerate 2-cocycle, and to a Manin triple of quadri-algebras associated to a nondegenerate invariant bilinear ...
Ni, Xiang, Bai, Chengming
openaire   +2 more sources

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

[Retracted] Double Weak Hopf Quiver and Its Path Coalgebra

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule structures on the said WHA are discussed.
Muhammad Naseer Khan, Munir Ahmed, Muhammad Arshad, Waleed Almutiry, Rashad A. R. Bantan, Mohammed Elgarhy, Muhammad Gulzar   +6 more
wiley   +1 more source