Jordan property for non-linear algebraic groups and projective varieties
By Sheng Meng, De-Qi Zhang. 2015
60 citations recorded by the source corpus.
Abstract:A century ago, Camille Jordan proved that the complex general linear group ${\rm GL}_n(\Bbb{C})$ has the Jordan property: there is a Jordan constant ${\rm C}_n$ such that every finite subgroup $H\le{\rm GL}_n(\Bbb{C})$ has an abelian subgroup $H_1$ of index $[H:H_1]\le{\rm C}_n$. We show that every connected algebraic group $G$ (which is not necessarily linear) has the Jordan property with the Jordan constant depending only on $\dim G$, and that the full automorphism group ${\rm Aut}(X)$ of every projective variety $X$ has the Jordan property.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/759efcf7a62d88c76c5a9c22f21a99e684f23c54
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Some structure theorems for algebraic groups (2015, background): “and references. Theorem 5.1.1 is due to Rosenlicht (see [Ro1, Cor. 5, p. 140]). This result is very useful for reducing questions about general algebraic groups to the linear and anti-affine cases; see [MZ] for a recent application. When char(k) = p>0, characterizing Lie algebras of smooth algebrai”