Lie Group behind a affine Lie algebra - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-20T10:05:13Z http://mathoverflow.net/feeds/question/87875 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87875/lie-group-behind-a-affine-lie-algebra Lie Group behind a affine Lie algebra Damien S. 2012-02-08T08:38:16Z 2012-02-08T09:14:20Z <blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/3061/constructing-affine-kac-moody-groups" rel="nofollow">Constructing Affine Kac-Moody Groups</a> </p> </blockquote> <p>Dear community,</p> <p>I have the following question about affine-type Lie algebras.</p> <p>In the finite-type Lie algebra, we associate to a root system a Lie algebra (or its enveloping algebra) that corresponds to a Lie group. For example, if we start from \$A_n\$ type, we have \$sl(n)\$, which is the Lie algebra of the group \$SL(n)\$.</p> <p>Now, I start from an affine Cartan matrix \$C\$ and I build an affine-type Lie algebra. Like above, I can build \$\widehat{sl}(n)\$. Is it the Lie algebra of a Lie group ? If yes, which one is it ? The infinite dimension of the Lie algebra makes things unclear to me...</p> <p>I accept both general answer and examples like in the \$sl(n)\$ case or even the \$sl(2)\$ case.</p> <p>Thank you for your comments,</p> <p>D.</p>