Abstract
Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have meaningful analogs for these groups and we establish a Jordan–Hölder type theorem that allows us to decompose any affine difference algebraic group into almost-simple affine difference algebraic groups. We also characterize almost-simple affine difference algebraic groups via almost-simple affine algebraic groups.
Original language | English |
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Pages (from-to) | 473–526 |
Number of pages | 54 |
Journal | Mathematische Zeitschrift |
Volume | 299 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - Oct 2021 |
Keywords
- Difference algebraic geometry
- Difference algebraic groups
- Difference Hopf algebras
ASJC Scopus subject areas
- General Mathematics