Results 21 to 30 of about 1,475 (226)
A combinatorial Hopf algebra for nonlinear output feedback control systems [PDF]
, 2014 In this work a combinatorial description is provided of a Faa di Bruno type Hopf algebra which naturally appears in the context of Fliess operators in nonlinear feedback control theory.
Luis A. Duffaut Espinosa +2 more
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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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The Hopf algebra of finite topologies and T-partitions [PDF]
, 2014 A noncommutative and noncocommutative Hopf algebra on finite topologies H_T is introduced and studied (freeness, cofreeness, self-duality...). Generalizing Stanley's definition of P-partitions associated to a special poset, we define the notion of T ...
L. Foissy, C. Malvenuto
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The tensor algebras of Yetter-Drinfeld module
上海师范大学学报. 自然科学版, 2014 The antipode of a Yetter-Drinfeld Hopf algebra is an anti-algebra and anti-coalgebra map is proved.It is also proved that the tensor algebra of Yetter-Drinfeld Hopf module is a Yetter-Drinfeld Hopf algebra.
Yanhua Wang
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The Hopf Algebra of Fliess Operators and Its Dual Pre-lie Algebra [PDF]
, 2013 We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finite-dimensional, connected grading. Dually, the vector space ℝ ⟨ x 0, x 1 ⟩ is both a pre-Lie algebra for the pre-
L. Foissy
semanticscholar +1 more source
Structure Theorems for Bicomodule Algebras Over Quasi-Hopf Algebras, Weak Hopf Algebras, and Braided Hopf Algebras [PDF]
Communications in Algebra, 2016 24 pages, many ...
Dello, Jeroen +3 more
openaire +3 more sources
Journal of Algebra, 2004 Let $K$ be a field of characteristic 0 containing all roots of unity. We classify all the Hopf structures on monomial $K$-coalgebras, or, in dual version, on monomial $K$-algebras.
Chen, Xiao-Wu +3 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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Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra [PDF]
, 2012 We give a natural and complete description of Ecalle's mould-comould formalism within a Hopf-algebraic framework. The arborification transform thus appears as a factorization of characters, involving the shuffle or quasishuffle Hopf algebras, thanks to a
Frédéric Fauvet, Frédéric Menous
semanticscholar +1 more source
International Journal of Mathematics and Mathematical Sciences, 2010 We introduce a class of noncommutative and noncocommutative weak Hopf algebras with infinite Ext quivers and study their structure. We decompose them into a direct sum of two algebras. The coalgebra structures of these weak Hopf algebras are described by
Dongming Cheng
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