Some topological properties of quotients modulo semisimple algebraic groups | Zendy

R. V. Gurjar | Zendy

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Some topological properties of quotients modulo semisimple algebraic groups

Author(s) -

R. V. Gurjar

Publication year - 2009

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/181

Subject(s) - mathematics , modulo , quotient , pure mathematics , topological group , algebraic number , topology (electrical circuits) , algebra over a field , discrete mathematics , combinatorics , mathematical analysis

We will prove a general result in Invariant Theory, viz. for a quotient C n ==G , where G is a connected complex semisimple algebraic group, the local first homology group at any point in the quotient C n ==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 C n ==G is a unique factorization domain (UFD).

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