Results 51 to 60 of about 1,418 (162)

Quantization of infinitesimal braidings and pre‐Cartier quasi‐bialgebras

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract In this paper, we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the nonsymmetric case. The algebraic counterpart of these categories is the notion of a pre‐Cartier quasi‐bialgebra, which extends the well‐known notion of quasi‐triangular quasi‐bialgebra given by Drinfeld.
Chiara Esposito, Andrea Rivezzi, Jonas Schnitzer, Thomas Weber   +3 more
wiley   +1 more source

Structure theorems for braided Hopf algebras

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley   +1 more source

The κ-(A)dS quantum algebra in (3+1) dimensions

Physics Letters B, 2017
The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group.
Ángel Ballesteros, Francisco J. Herranz, Fabio Musso, Pedro Naranjo   +3 more
doaj   +1 more source

A coboundary Temperley–Lieb category for sl2$\mathfrak {sl}_{2}$‐crystals

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract By considering a suitable renormalization of the Temperley–Lieb category, we study its specialization to the case q=0$q=0$. Unlike the q≠0$q\ne 0$ case, the obtained monoidal category, TL0(k)$\mathcal {TL}_0(\mathbb {k})$, is not rigid or braided. We provide a closed formula for the Jones–Wenzl projectors in TL0(k)$\mathcal {TL}_0(\mathbb {k})$
Moaaz Alqady, Mateusz Stroiński
wiley   +1 more source

Double Copy From Tensor Products of Metric BV■‐Algebras

Fortschritte der Physik, Volume 73, Issue 1-2, February 2025.
Abstract Field theories with kinematic Lie algebras, such as field theories featuring color–kinematics duality, possess an underlying algebraic structure known as BV■‐algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV■‐algebra.
Leron Borsten, Branislav Jurčo, Hyungrok Kim, Tommaso Macrelli, Christian Saemann, Martin Wolf   +5 more
wiley   +1 more source

Tubings, chord diagrams, and Dyson–Schwinger equations

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract We give series solutions to single insertion place propagator‐type systems of Dyson–Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a straightforward contribution.
Paul‐Hermann Balduf, Amelia Cantwell, Kurusch Ebrahimi‐Fard, Lukas Nabergall, Nicholas Olson‐Harris, Karen Yeats   +5 more
wiley   +1 more source

Quantization of the Rank Two Heisenberg–Virasoro Algebra

Axioms
Quantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras.
Xue Chen
doaj   +1 more source

Novel non‐involutive solutions of the Yang–Baxter equation from (skew) braces

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We produce novel non‐involutive solutions of the Yang–Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew braces, and surprisingly in the case of braces, they are not necessarily involutive.
Anastasia Doikou, Bernard Rybołowicz
wiley   +1 more source

Near braces and p$p$‐deformed braided groups

Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 124-139, January 2024.
Abstract Motivated by recent findings on the derivation of parametric noninvolutive solutions of the Yang–Baxter equation, we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new multi‐parametric, nondegenerate, noninvolutive solutions of the set‐theoretic Yang–Baxter equation.
Anastasia Doikou, Bernard Rybołowicz
wiley   +1 more source

Bialgebraic Structures And Smarandache Bialgebraic Structures

, 2003
The study of bialgebraic structures started very recently. Till date there are no books solely dealing with bistructures. The study of bigroups was carried out in 1994-1996. Further research on bigroups and fuzzy bigroups was published in 1998. In the year 1999, bivector spaces was introduced.
openaire   +4 more sources