Alexander Zimmermann

activity

20222025

collaborators

5 papers

math.RA2025

DG-Semiprimary DG-Algebras, Acyclicity and Hopkins-Levitzki Theorem for DG-Algebras

Alexander Zimmermann

We study the analogue of the Hopkins-Levitzky Theorem for dg-algebras $(A, d)$ . We first consider the Hopkins approach. Here we show that for acyclic dg-algebras with graded-Artinia…

math.RA2024

Differential graded division algebras, their modules, and dg-simple algebras

Alexander Zimmermann

We give the definition of a dg-division algebra, that is a concept of a differential graded algebra which may serve as an analogue of a division algebra. We classify them completel…

math.RA2023

Ore Localisation for differential graded rings; Towards Goldie's theorem for differential graded algebras

Alexander Zimmermann

We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essent…

math.RA2023

Differential graded orders, their class groups and idèles

Alexander Zimmermann

For a Dedekind domain $R$ with field of fractions $K$ a classical $R$ -order in a semisimple $K$ -algebra $A$ is an $R$ -projective $R$ -subalgebra $Λ$ of $A$ such that $K Λ = A$ . We stud…

math.RT2022

Clifford's theorem for orbit categories

Alexander Zimmermann

Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors.…