Differential graded division algebras, their modules, and dg-simple algebras
Abstract
We give the definition of a dg-division algebra, that is a concept of a differential graded algebra which can serve as an analogue of a division algebra. We classify them completely, and show that they are either acyclic or have differential 0. Furthermore, we prove that the graded centre of dg-simple dg-algebras is a dg-division algebra, and also that the dg-endomorphism ring of a dg-simple module is a dg-division algebra. We will also give a Jacobson-Chevalley density theorem for acyclic dg-algebras.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Polynomial and algebraic computation
Publication details
- Journal / source
- Mathematica
- Volume
- 68 (91)
- Issue
- 1
- Pages
- 146–160
- Publication date
- 30 June 2026
- Language
- EN