Structure of connected nested automorphism groups

2023/12/13 by Perepechko, Alexander · 2 citations
#14J50 #14R20 (Primary) 14L40 #22E65 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.08359

Abstract

A nested group is an increasing union of a sequence of algebraic groups. In this paper, we describe maximal nested unipotent subgroups of Aut(X), where X is an affine variety. It turns out that they are similar to the group of triangular automorphisms of \mathbbAⁿ. We show that if an abstract subgroup of Aut(X) consists of unipotent elements, then it is closed if and only if it is nested. This implies that a connected nested subgroup of Aut(X) is closed, answering a question of Kraft and Zaidenberg (2022, arXiv:2203.11356). We also extend the recent description of maximal commutative unipotent subgroups by Regeta and van Santen (2024, arXiv:2112.04784), offering a direct construction method and relating them to our description.

Cited by

• Borel subalgebras of Lie algebras of vector fields
• Borel subgroups of the automorphism groups of affine toric surfaces

Related

• Maximal commutative unipotent subgroups and a characterization of affine spherical varieties
• On the maximality of the triangular subgroup
• On the automorphism group of a toral variety
• When is the automorphism group of an affine variety linear?
• Embeddings of groups \rm Aut(F_n) into automorphism groups of algebraic varieties