Results 71 to 80 of about 28,962 (144)
Genus bounds from unrolled quantum groups at roots of unity
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract For any simple complex Lie algebra g$\mathfrak {g}$, we show that the degrees of the “ADO” link polynomials coming from the unrolled restricted quantum group U¯qH(g)$\overline{U}^H_q(\mathfrak {g})$ at a root of unity give lower bounds to the Seifert genus of the link.
Daniel López Neumann +1 more
wiley +1 more source
Asymmetric graphs with quantum symmetry
Proceedings of the London Mathematical Society, Volume 131, Issue 5, November 2025.Abstract We present an infinite sequence of finite graphs with trivial automorphism group and non‐trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are the first examples of any asymmetric classical space that has non‐trivial quantum symmetries.
Josse van Dobben de Bruyn +2 more
wiley +1 more source
Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
, 2006 Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras.
Ebrahimi-Fard, Kurusch, Guo, Li
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A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions [PDF]
Annals of Combinatorics, 2002 A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra structure of the MacMahon symmetric functions relying on the construction of a Hopf algebra from any alphabet of neutral letters ...
Rosas Celis, Mercedes Helena +2 more
openaire +4 more sources
Engineering Reports, Volume 7, Issue 10, October 2025.This work presents a secure telemedicine cryptosystem based on a novel 4D memristive chaotic oscillator and a Dispatched Gray Code Scrambler (DGCS). Implemented on FPGA, the system ensures power‐efficient encryption, making it suitable for real‐time medical image transmission in IoT healthcare environments.
Fritz Nguemo Kemdoum +3 more
wiley +1 more source
(Non)Commutative Hopf algebras of trees and (quasi)symmetric functions [PDF]
, 2007 The Connes-Kreimer Hopf algebra of rooted trees, its dual, and the Foissy Hopf algebra of of planar rooted trees are related to each other and to the well-known Hopf algebras of symmetric and quasi-symmetric functions via a pair of commutative diagrams ...
Hoffman, Michael E.
core
Holomorphic field theories and higher algebra
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley +1 more source
Combinatorial Hopf algebra of supercharacters of type D [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We provide a Hopf algebra structure on the supercharacter theory for the unipotent upper triangular group of type {D} over a finite field. Also, we make further comments with respect to types {B} and {C}. Type {A} was explored by M. Aguiar et. al (2010), thus this extended abstract is a contribution to understand combinatorially the supercharacter ...
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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
Hopf algebra structures in particle physics
, 2003 In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.Comment: 6 pages, talk ...
Weinzierl, Stefan
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