Results 1 to 10 of about 95 (92)
Axioms, 2012 Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2)/2ab = ((a’)^2+(b’)^2-(c’))^2/2a’b’ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a ...
Jeffrey R. Schmidt
exaly +3 more sources
Rota–Baxter (Co)algebra Equation Systems and Rota–Baxter Hopf Algebras
Mathematics, 2022 We introduce and discuss the notions of Rota–Baxter bialgebra equation systems and Rota–Baxter Hopf algebras. Then we construct a lot of examples based on Hopf quasigroups.
Yue Gu, Shuanhong Wang, Tianshui Ma
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Drinfel’d double symmetry of the 4d Kitaev model
Journal of High Energy Physics, 2023 Following the general theory of categorified quantum groups developed by the author previously, we construct the Drinfel’d double 2-bialgebra associated to a finite group N = G 0.
Hank Chen
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Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra
Mathematics, 2023 The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations.
Yihong Su, Xue Chen
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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
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Hopf algebra of permutation pattern functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We study permutation patterns from an algebraic combinatorics point of view. Using analogues of the classical shuffle and infiltration products for word, we define two new Hopf algebras of permutations related to the notion of permutation pattern.
Yannic Vargas
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SciPost Physics, 2021 We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi--Lie bialgebra, extending the known correspondence between a Lie ...
Jose J. Fernandez-Melgarejo, Yuho Sakatani
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Algebraic theories of power operations
Journal of Topology, Volume 16, Issue 4, Page 1543-1640, December 2023., 2023 Abstract We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well‐behaved theories of power operations for E∞$\mathbb {E}_\infty$ ring spectra.
William Balderrama
wiley +1 more source
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 +2 more
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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
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