The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

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