Results 21 to 30 of about 145 (139)

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

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

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

On the bialgebra of functional graphs and differential algebras [PDF]

Discrete Mathematics & Theoretical Computer Science, 1997
We develop the bialgebraic structure based on the set of functional graphs, which generalize the case of the forests of rooted trees. We use noncommutative polynomials as generating monomials of the functional graphs, and we introduce circular and ...
Maurice Ginocchio
doaj   +3 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

GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS [PDF]

Glasgow Mathematical Journal, 2013
AbstractMalvenuto and Reutenauer (C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra177 (1995), 967–982) showed how the total symmetric group ring ⊕nZΣn could be made into a Hopf algebra with a very nice structure which admitted the Solomon descent algebra as a sub-Hopf algebra.
openaire   +4 more sources

[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