arXiv subjects

Can Hatipoğlu

Publications and source records attributed to Can Hatipoğlu.

3 recordsLinked to original sources

arXiv2026

Iterated Hopf Ore Extensions over Group Rings

We introduce and study a class of Hopf algebras $H(G, χ, η, b, c, β)$ which are two-step Ore extensions of a group algebra $\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as generalized Taft algebras and Hopf algebras related to $\mathfrak{sl}_2$ constructed by Wang, Wu, and Tan. We analyze the ring theoretical properties of these algebras and classify all finite dimensional simple modules over them. We also consider the tensor products of simple modules in the zero derivation case.

math.RA↗

arXiv2021

Locally Finite Representations Over Noetherian Hopf algebras

We study finite dimensional representations over some Noetherian algebras over a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category of locally finite dimensional representations to be closed under taking injective hulls and extend results known for group rings and enveloping algebras to Ore extensions, Hopf crossed products and affine Hopf algebras of low Gelfand-Kirillov dimension.

math.RT↗

arXiv2014

Stable torsion theories and the injective hulls of simple modules

A torsion theoretical characterization of left Noetherian rings $R$ over which injective hulls of simple left modules are locally Artinian is given. Sufficient conditions for a left Noetherian ring to satisfy this finiteness condition are obtained in terms of torsion theories.

math.RA↗