Natural endomorphisms of quasi-shuffle Hopf algebras

Jean-Christophe Novelli; Frédéric Patras; Jean-Yves Thibon

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Displaying similar documents to “Natural endomorphisms of quasi-shuffle Hopf algebras”

Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras

Christian Kassel (2013)

Annales mathématiques Blaise Pascal

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We define polynomial $H$ -identities for comodule algebras over a Hopf algebra $H$ and establish general properties for the corresponding $T$ -ideals. In the case $H$ is a Taft algebra or the Hopf algebra $E (n)$ , we exhibit a finite set of polynomial $H$ -identities which distinguish the Galois objects over $H$ up to isomorphism.

On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

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Quasi-algebraic representability of sets in $R^{n}$ .

W. Waliszewski (1984)

Banach Center Publications

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Cobraided smash product Hom-Hopf algebras

Tianshui Ma, Haiying Li, Tao Yang (2014)

Colloquium Mathematicae

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Let (A,α) and (B,β) be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: R-smash products $(A ♮_{R} B, α \otimes β)$ . Moreover, necessary and sufficient conditions for $(A ♮_{R} B, α \otimes β)$ to be a cobraided Hom-Hopf algebra are given.

The duality theorem for twisted smash products of Hopf algebras and its applications

Zhongwei Wang, Liangyun Zhang (2015)

Colloquium Mathematicae

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Let $A_{T} H$ denote the twisted smash product of an arbitrary algebra A and a Hopf algebra H over a field. We present an analogue of the celebrated Blattner-Montgomery duality theorem for $A_{T} H$ , and as an application we establish the relationship between the homological dimensions of $A_{T} H$ and A if H and its dual H* are both semisimple.

Fine and quasi connectedness in nonlinear potential theory

David R. Adams, John L. Lewis (1985)

Annales de l'institut Fourier

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If $B_{α, p}$ denotes the Bessel capacity of subsets of Euclidean $n$ -space, $α > 0$ , $1 < p < \infty$ , naturally associated with the space of Bessel potentials of $L^{p}$ -functions, then our principal result is the estimate: for $1 < α p \leq n$ , there is a constant $C = C (α, p, n)$ such that for any set $E$ $min {B_{α, p} (E \cap Q), B_{α, p} (E^{c} \cap Q)} \leq C \cdot B_{α, p} (Q \cap \partial_{f} E)$ for all open cubes $Q$ in $n$ -space. Here $\partial_{f} E$ is the boundary of the $E$ in the $(α, p)$ -fine topology i.e. the smallest topology on $c$ -space that makes the associated $(α, p)$ -linear potentials continuous there. As a consequence,...

$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

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Symmetries in connected graded algebras and their PBW-deformations

Yongjun Xu, Xin Zhang (2023)

Czechoslovak Mathematical Journal

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We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo’s quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a $𝒦_{2}$ algebra $𝒜$ which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra ${ℱ𝒦}_{3}$ , and explicitly construct all the (self-)symmetric and sign-(self-)symmetric...

$𝔤$ -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

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A Lie version of Turaev’s $\bar{G}$ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a $𝔤$ -quasi-Frobenius Lie algebra for $𝔤$ a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra $(𝔮, β)$ together with a left $𝔤$ -module structure which acts on $𝔮$ via derivations and for which $β$ is $𝔤$ -invariant. Geometrically, $𝔤$ -quasi-Frobenius Lie algebras are the Lie algebra structures associated to...

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel&#039;yanov, Manfred P. H. Wolff (2001)

Studia Mathematica

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Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace $X ₀ : = x \in X : l i m_{n \to \infty} | | T ⁿ x | | = 0$ is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness $χ_{| | \cdot | | ₁} (A) < 1$ for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove...