Results 71 to 80 of about 680,985 (272)
On indicators of Hopf algebras [PDF]
Israel Journal of Mathematics, 2015 Kashina, Montgomery and Ng introduced the $n$-th indicator $ν_n(H)$ of a finite-dimensional Hopf algebra $H$ and showed that the indicators have some interesting properties such as the gauge invariance. The aim of this paper is to investigate the properties of $ν_n$'s. In particular, we obtain the cyclotomic integrality of $ν_n$ and a formula for $ν_n$
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Ore Extensions of Multiplier Hopf Coquasigroups
AxiomsThis paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups.
Rui Zhang +3 more
doaj +1 more source
Universal enveloping algebras of Poisson Hopf algebras [PDF]
, 2014 For a Poisson algebra $A$, by exploring its relation with Lie-Rinehart algebras, we prove a Poincar\'e-Birkoff-Witt theorem for its universal enveloping algebra $A^e$.
Jia-Feng Lu, Xingting Wang, G. Zhuang
semanticscholar +1 more source
Journal of Algebra, 2004 If \(Q\) is a Schurian Hopf quiver and \(k\) is a field of characteristic zero, the simple pointed Hopf subalgebras of a graded Hopf algebra structure on the path coalgebra \(kQ^c\) are classified. A dual Gabriel theorem for pointed Hopf algebras is proved.
Van Oystaeyen, Fred, Zhang, Pu
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Redfield-Pólya theorem in $\mathrm{WSym}$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give noncommutative versions of the Redfield-Pólya theorem in $\mathrm{WSym}$, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras.
Jean-Paul Bultel +3 more
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T(w)o Patch or Not T(w)o Patch: A Novel Biocontrol Model
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT A number of top‐down biocontrol models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest‐dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest‐dependent
Urvashi Verma +2 more
wiley +1 more source
EPiC Series in Computing, 2018 Classically, Hopf algebras are defined on the basis of modules over commutative rings. The present study seeks to extend the Hopf algebra formalism to a more general universal-algebraic setting, entropic varieties, including (pointed) sets, barycentric algebras, semilattices, and commutative monoids.
Anna B. Romanowska, Jonathan D. H. Smith
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Rota-Baxter Leibniz Algebras and Their Constructions
Advances in Mathematical Physics, 2018 In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and ...
Liangyun Zhang, Linhan Li, Huihui Zheng
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Convolution Powers of the Identity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study convolution powers $\mathtt{id}^{\ast n}$ of the identity of graded connected Hopf algebras $H$. (The antipode corresponds to $n=-1$.) The chief result is a complete description of the characteristic polynomial - both eigenvalues and ...
Marcelo Aguiar, Aaron Lauve
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Primitive Cohomology of Hopf algebras [PDF]
, 2014 Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented.
D. Wang, James J. Zhang, G. Zhuang
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