Infinitely transitive actions on real affine suspensions

TL;DR

This paper demonstrates that under certain conditions, the property of infinite transitivity of the special automorphism group on a real affine variety Y extends to its affine suspensions, broadening previous results.

Contribution

It generalizes the known infinite transitivity property from a variety Y to its affine suspensions over the real numbers, under mild restrictions.

Findings

Infinite transitivity extends from Y to its affine suspensions.

The result applies to varieties with dimension ≥ 2.

Generalizes previous work over the real field.

Abstract

A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y. Given a real affine algebraic variety Y of dimension greater than or equal to two, we show that, under a mild restriction, if the special automorphism group of Y (the group generated by one-parameter unipotent subgroups) is infinitely transitive on each connected component of the smooth locus of Y, then for any real affine suspension X over Y, the special automorphism group of X is infinitely transitive on each connected component of the smooth locus of X. This generalizes a recent result by Arzhantsev, Kuyumzhiyan and Zaidenberg over the field of real numbers.