Results 31 to 40 of about 1,418 (162)

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

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

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

Quasitriangular Structure of Myhill–Nerode Bialgebras

Axioms, 2012
In computer science the Myhill–Nerode  Theorem states that a set L of words in a finite alphabet is accepted by a finite automaton if and only if the equivalence relation ∼L, defined  as x ∼L  y if and only if xz ∈ L exactly when yz ∈ L, ∀z, has finite ...
Robert G. Underwood
doaj   +1 more source

Polyadic Hopf Algebras and Quantum Groups

East European Journal of Physics, 2021
This article continues the study of concrete algebra-like structures in our polyadic approach, where the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some natural ...
S. Duplij
doaj   +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

Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras

Mathematics, 2020
The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic).
Xiaohong Zhang, Xiangyu Ma, Xuejiao Wang
doaj   +1 more source