Ramy Yammine

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Eliezer Batista

Aks GK

Eetp 455

Deividi Pansera

Faculdade de Ciências da Universidade do Porto

University of Glasgow

Martin Bordemann

Université de Haute-Alsace (UHA)

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Papers by Ramy Yammine

Representations and actions of Hopf algebras

The larger area of my thesis is Algebra; more specifically, my work belongs to the following two ... more The larger area of my thesis is Algebra; more specifically, my work belongs to the following two major branches of Algebra: \emph{representation theory} and \emph{invariant theory}. In brief, the objective of representation theory is to investigate algebraic objects through their actions on vector spaces; this allows the well-developed toolkit of linear algebra to be brought to bear on complex algebraic problems. The theory has played a crucial role in nearly every subdiscipline of pure mathematics. Outside of pure mathematics, representation theory has been successfully used, for instance, in the study of symmetries of physical systems and in describing molecular structures in physical chemistry. Invariant theory is another classical algebraic theme permeating virtually all areas of pure mathematics and some areas of applied mathematics as well, notably coding theory. The theory studies actions of algebraic objects, traditionally groups and Lie algebras, on algebras, that is, vecto...

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Actions of cocommutative Hopf algebras

Journal of Algebra, 2019

Let H be a cocommutative Hopf algebra acting on an algebra A. Assuming the base field to be algeb... more 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 coaction of some Hopf subalgebra of the finite dual H • that is an integral domain, we stratify the prime spectrum Spec A in terms of the prime spectra of certain commutative algebras. For arbitrary H-actions in characteristic 0, we show that the largest H-stable ideal of A that is contained in a given semiprime ideal of A is semiprime as well.

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On representations of connected Hopf algebras

arXiv: Rings and Algebras, 2020

Let $H$ be a connected Hopf algebra acting on an algebra $A$. Working over a base field having ch... more Let $H$ be a connected Hopf algebra acting on an algebra $A$. Working over a base field having characteristic $0$, we show that for a given prime (semi-prime, completely prime) ideal $I$ of $A$, the largest $H$-stable ideal of A contained in $I$ is also prime (semi-prime, completely prime). We also prove a similar result for certain subrings of convolution algebras.

On the adjoint representation of a hopf algebra

We consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part,... more

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On actions of connected Hopf algebras

Proceedings of the American Mathematical Society

Let H H be a connected Hopf algebra acting on an algebra A A . Working over a base field having c... more Let H H be a connected Hopf algebra acting on an algebra A A . Working over a base field having characteristic 0 0 , we show that for a given prime (semi-prime, completely prime) ideal I I of A A , the largest H H -stable ideal of A contained in I I is also prime (semi-prime, completely prime). We also prove a similar result for certain subrings of convolution algebras.

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