Results 21 to 30 of about 1,418 (162)
Discrete Mathematics & Theoretical Computer Science, 2015 We define a $K$ -theoretic analogue of Fomin’s dual graded graphs, which we call dual filtered graphs. The key formula in the definition is $DU - UD = D + I$.
Rebecca Patrias, Pavlo Pylyavskyy
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Quantifier Scope in Categorical Compositional Distributional Semantics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 In previous work with J. Hedges, we formalised a generalised quantifiers theory of natural language in categorical compositional distributional semantics with the help of bialgebras.
Mehrnoosh Sadrzadeh
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The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras
Mathematics, 2022 In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras.
Shuangjian Guo +2 more
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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 +1 more
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, 2022 We introduce the notion of a quadri-bialgebra, which gives a bialgebra theory for the quadri-algebra introduced by Aguiar and Loday. We show that a quadri-bialgebra is equivalent to a Manin triple of dendriform algebras associated to a nondegenerate 2-cocycle, and to a Manin triple of quadri-algebras associated to a nondegenerate invariant bilinear ...
Ni, Xiang, Bai, Chengming
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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
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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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The ZX calculus is a language for surface code lattice surgery [PDF]
Quantum, 2020 A leading choice of error correction for scalable quantum computing is the surface code with lattice surgery. The basic lattice surgery operations, the merging and splitting of logical qubits, act non-unitarily on the logical states and are not easily ...
Niel de Beaudrap, Dominic Horsman
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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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3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
Mathematics, 2022 In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-Hom–Lie algebras.
Shuangjian Guo +2 more
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