Reality Properties of Conjugacy Classes in G_2
| dc.creator | Singh, Anupam | |
| dc.creator | Thakur, Maneesh | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T09:31:02Z | |
| dc.date.available | 2026-07-07T09:31:02Z | |
| dc.description | Let $G$ be an algebraic group over a field $k$. We call $g\in G(k)$ {\bf real} if $g$ is conjugate to $g^{-1}$ in $G(k)$. In this paper we study reality for groups of type $G_2$ over fields of characteristic different from 2. Let $G$ be such a group over $k$. We discuss reality for both semisimple and unipotent elements. We show that a semisimple element in $G(k)$ is real if and only if it is a product of two involutions in $G(k)$. Every unipotent element in $G(k)$ is a product of two involutions in $G(k)$. We discuss reality for $G_2$ over special fields and construct examples to show that reality fails for semisimple elements in $G_2$ over $\Q$ and $\Q_p$. We show that semisimple elements are real for $G_2$ over $k$ with $cd(k)\leq 1$. We conclude with examples of nonreal elements in $G_2$ over $k$ finite, with characteristic $k$ not 2 or 3, which are not semisimple or unipotent. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0804.1243 | |
| dc.identifier | http://arxiv.org/abs/0804.1243 | |
| dc.identifier | Israel Journal of Mathematics 145 (2005) 157-192 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158320 | |
| dc.subject | Group Theory | |
| dc.subject | 20G15, 17A75 | |
| dc.title | Reality Properties of Conjugacy Classes in G_2 | |
| dc.type | text |