Commentarii Mathematici Helvetici


Full-Text PDF (165 KB) | Metadata | Table of Contents | CMH summary
Volume 84, Issue 4, 2009, pp. 793–806
DOI: 10.4171/CMH/181

Published online: 2009-12-23

Some topological properties of quotients modulo semisimple algebraic groups

R. V. Gurjar[1]

(1) Tata Institute of Fundamental Research, Bombay, India

We will prove a general result in Invariant Theory, viz. for a quotient ℂn//G, where G is a connected complex semisimple algebraic group, the local first homology group at any point in the quotient ℂn//G is trivial and the local second homology group is finite. Using this we will prove that the completion of the local ring of any point in ℂn//G is a unique factorization domain (UFD).

Keywords: Semisimple algebraic group, quotient, homology group

Gurjar R.: Some topological properties of quotients modulo semisimple algebraic groups. Comment. Math. Helv. 84 (2009), 793-806. doi: 10.4171/CMH/181