Cherlin's conjecture for almost simple groups of Lie rank 1

Thompson’s conjecture for real semi-simple Lie groups

A proof of Thompson’s conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic geometry.

OD-characterization of almost simple groups related to U3(11)

Let $L := U_3(11)$. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. In fact, we prove that $L$, $L:2$ and $L:3$ are OD-characterizable, and $L:S_3$ is $5$-fold OD-characterizable.

Almost commuting elements in compact Lie groups

Almost-Riemannian Geometry on Lie Groups

A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) − 1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS’s, and these results are illustrated by examples on the 2D affine and the Heisenberg groups. These ARS’s are extended in two wa...

Almost Integral Tqfts from Simple Lie Algebras

Almost integral TQFT was introduced by Gilmer [G]. For each simple Lie algebra g and some prime integer we associate an almost integral TQFT which derives the projective Witten-Reshetikhin-Turaev invariant τ for closed 3-manifolds. As a corollary, one can show that τ is an algebraic integer for certain prime integers. The result in this paper can be used to prove that τ M satisfies some Murasug...