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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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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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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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Classical Lie bialgebras for AdS/CFT integrability by contraction and reduction
SciPost Physics, 2023 Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra.
Niklas Beisert, Egor Im
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Quasitriangular Structure of Myhill–Nerode Bialgebras
Axioms, 2012 In computer science the Myhill–Nerode Theorem states that a set L of words in a finite alphabet is accepted by a finite automaton if and only if the equivalence relation ∼L, defined as x ∼L y if and only if xz ∈ L exactly when yz ∈ L, ∀z, has finite ...
Robert G. Underwood
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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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