Computing centralizers in Lie groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T16:26:23Z http://mathoverflow.net/feeds/question/67469 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/67469/computing-centralizers-in-lie-groups Computing centralizers in Lie groups J Newman 2011-06-10T20:20:06Z 2011-06-10T20:20:06Z <p>Let $G$ be a real semisimple Lie group. Really, I only care about $\text{SL}(n,\mathbb{R})$ and $\text{Sp}(2n,\mathbb{R})$.</p> <p>I'd like to perform a computer search for a finite group with a certain property (that property is not important here). To do this, I need to be able to efficiently compute the isomorphism classes (as Lie groups) of the centralizers of certain finite subgroups of $G$. The finite groups involved might be rather large.</p> <p>This brings me to two related questions. First, where can I find algorithms for this? Second, what would be the best form in which to generate my finite subgroups? For instance, is it fine to just give generators, should I give a list of all the matrices in the finite group, do I also need a presentation of the finite groups, etc?</p>