Results 11 to 20 of about 95 (92)

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

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

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

[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

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   +2 more sources

Presenting Finite Posets [PDF]

Electronic Proceedings in Theoretical Computer Science, 2015
We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively.
Samuel Mimram
doaj   +1 more source

Quantization of the Super‐BMS3 Algebra

Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022
In this article, we study quantization of super‐BMS3 algebra W. We quantize W by the Drinfel’d twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras.
Yu Yang, Xing Tao Wang, Francesco Toppan
wiley   +1 more source

Weak Hopf Algebra and Its Quiver Representation

Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021
This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so‐called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representation for each weak Hopf quiver.
Muhammad Naseer Khan, Ahmed Munir, Muhammad Arshad, Ahmed Alsanad, Suheer Al-Hadhrami, Dragan Pamučar   +5 more
wiley   +1 more source