Results 1 to 10 of about 41,471 (142)
A Hopf algebra of subword complexes (Extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces ...
Nantel Bergeron, Cesar Ceballos
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A pair of dual Hopf algebras on permutations
AIMS Mathematics, 2021 Hopf algebras are important objects in algebraic combinatorics since they have strong stability. In particular, its dual space is an important tool to study the properties of the original Hopf algebra.
Mingze Zhao, Huilan Li
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Discrete Mathematics & Theoretical Computer Science, 2014 A general lattice theoretic construction of Reading constructs Hopf subalgebras of the Malvenuto-Reutenauer Hopf algebra (MR) of permutations. The products and coproducts of these Hopf subalgebras are defined extrinsically in terms of the embedding in MR.
Shirley Law
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The Incidence Hopf Algebra of Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions.
Brandon Humpert, Jeremy L. Martin
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Algebraic and combinatorial structures on Baxter permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (\emphi.e.
Samuele Giraudo
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Amplitudes, Hopf algebras and the colour-kinematics duality
Journal of High Energy Physics, 2022 It was recently proposed that the kinematic algebra featuring in the colour-kinematics duality for scattering amplitudes in heavy-mass effective field theory (HEFT) and Yang-Mills theory is a quasi-shuffle Hopf algebra.
Andreas Brandhuber +5 more
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Renormalization of gauge fields: A Hopf algebra approach [PDF]
, 2006 We study the Connes-Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov-Taylor identities (in the abelian and non-abelian case respectively) are compatible with the Hopf algebra ...
van Suijlekom, Walter D.
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Combinatorial Hopf Algebras of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra.
Carolina Benedetti +2 more
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Coloured peak algebras and Hopf algebras [PDF]
, 2005 For $G$ a finite abelian group, we study the properties of general equivalence relations on $G_n=G^n\rtimes \SG_n$, the wreath product of $G$ with the symmetric group $\SG_n$, also known as the $G$-coloured symmetric group.
A. Björner +16 more
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Post-Lie algebras in Regularity Structures
Forum of Mathematics, Sigma, 2023 In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra.
Yvain Bruned, Foivos Katsetsiadis
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