Hopf Ore Extensions
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DOI: 10.1007/s10468-019-09901-8
Abstract: Brown, O’Hagan, Zhang, and Zhuang gave a set of conditions on an automorphism σ and a σ-derivation δ of a Hopf k-algebra R for when the skew polynomial extension T = R[x,σ,δ] of R admits… read more here.
Keywords: hopf; hopf algebra; extensions hopf; hopf ore ... See more keywords
The Dual and the Double of a Hopf Algebroid are Hopf Algebroids
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DOI: 10.1007/s10485-015-9418-7
Abstract: Let H be a ×-bialgebra in the sense of Takeuchi. We show that if H is ×-Hopf, and if H fulfills the finiteness condition necessary to define its skew dual H∨, then the coopposite of… read more here.
Keywords: algebroid hopf; hopf; hopf algebroid; double hopf ... See more keywords
Delay-induced Hopf and double Hopf-bifurcation in plankton system with dormancy of predators
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DOI: 10.1007/s11071-021-06617-7
Abstract: In this article, we propose a model for plankton dynamics in presence of dormancy and time delay. Dormancy is a better adaptive strategy to survive in a harsh environmental condition than active ones. The dormancy… read more here.
Keywords: system; dormancy; hopf; plankton ... See more keywords
Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting
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DOI: 10.1007/s40840-018-0624-y
Abstract: In this paper, we introduce the notion of weak nonassociative Doi–Hopf module and give the Fundamental Theorem of Hopf modules in this setting. Also, we prove that there exists a categorical equivalence that admits as… read more here.
Keywords: theorems doi; hopf modules; hopf; modules nonassociative ... See more keywords
Generalized Hopf–Ore extensions
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DOI: 10.1016/j.jalgebra.2018.04.032
Abstract: We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized… read more here.
Keywords: hopf; ore extension; hopf ore; generalized hopf ... See more keywords
Actions of cocommutative Hopf algebras
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DOI: 10.1016/j.jalgebra.2019.11.010
Abstract: Let $H$ be a cocommutative Hopf algebra acting on an algebra $A$. Assuming the base field to be algebraically closed and the $H$-action on $A$ to be integral, that is, it is given by a… read more here.
Keywords: actions cocommutative; hopf; algebra; cocommutative hopf ... See more keywords
A note on the discriminant of reflection Hopf algebras
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DOI: 10.1016/j.jalgebra.2022.04.009
Abstract: We provide a formula for commputing the discriminant of skew Calabi-Yau algebra over a central Calabi-Yau algebra. This method is applied to study the Jacobian and discriminant for reflection Hopf algebras. Introduction Recently, the discriminant… read more here.
Keywords: calabi yau; hopf; algebra; reflection ... See more keywords
Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra
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DOI: 10.1063/5.0031135
Abstract: We introduce a Hopf algebra structure on the N = 2 quantum supersymmetry algebra and formulate a first order quantum differential calculus on it. Then, it is enhanced to three *-calculi by defining three appropriate… read more here.
Keywords: quantum; algebra; hopf; quantum super ... See more keywords
Morita equivalence for weak Hopf–Galois extensions
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DOI: 10.1080/00927872.2016.1175572
Abstract: ABSTRACT Let H be a commutative weak Hopf algebra over a fixed field k, and A,B be weak H-Hopf Galois extensions. In this paper, we give a structure theorem for the category of weak relative… read more here.
Keywords: hopf; galois extensions; hopf galois; weak hopf ... See more keywords
On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property
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DOI: 10.1080/00927872.2018.1508582
Abstract: Abstract Let be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over whose Hopf coradical is isomorphic to the unique 12-dimensional Hopf algebra without the dual Chevalley property, such that… read more here.
Keywords: algebra without; hopf; unique dimensional; dimensional hopf ... See more keywords
Bounded global Hopf branches for stage-structured differential equations with unimodal feedback
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DOI: 10.1088/1361-6544/aa5497
Abstract: We consider a class of stage-structured differential equations with unimodal feedback. By using the time delay as a bifurcation parameter, we show that the number of local Hopf bifurcation values is finite. Furthermore, we analytically… read more here.
Keywords: global hopf; hopf; structured differential; bounded global ... See more keywords