Arithmetic groups of gauge transformations

Arithmetic groups of gauge transformations Abstract. Linear groups over many finitely generated Z-algebras are realized äs groups of ftmctions over varieties. We show that this construction produces a large number of explicit K ( , l)'s which are infinite dimensional double coset spaces. 1991 Mathematics Subject Classification: 55R35, 20G30, 58B05, 58B25. Introduction The class of linear groups = G (A) over finitely generated Z-algebras A includes the arithmetic groups äs well äs many which are less tractable, e.g. many groups of infinite virtual cohomological dimension. This paper shows that many linear groups = G (A) act äs covering transformations or branched covering transformations on coset spaces of groups of maps, generalizing constructions familiär for arithmetic groups. These classifying spaces may also be viewed äs quotients of spaces of maps into finite-dimensional Symmetrie spaces, and this description gives our spaces attractive geometric properties, such äs curvatures which are computable for certain mapping functors by the methods of the appendix to [FG]. The groups of maps considered here may be viewed äs the Ä-points of a linear algebraic group, where R is a subring of the coordinate ring of an affine variety, and this paper offers a characterization of a good class of rings R http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Arithmetic groups of gauge transformations

Forum Mathematicum, Volume 5 (5) – Jan 1, 1993

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1993.5.49
Publisher site
See Article on Publisher Site

Abstract

Abstract. Linear groups over many finitely generated Z-algebras are realized äs groups of ftmctions over varieties. We show that this construction produces a large number of explicit K ( , l)'s which are infinite dimensional double coset spaces. 1991 Mathematics Subject Classification: 55R35, 20G30, 58B05, 58B25. Introduction The class of linear groups = G (A) over finitely generated Z-algebras A includes the arithmetic groups äs well äs many which are less tractable, e.g. many groups of infinite virtual cohomological dimension. This paper shows that many linear groups = G (A) act äs covering transformations or branched covering transformations on coset spaces of groups of maps, generalizing constructions familiär for arithmetic groups. These classifying spaces may also be viewed äs quotients of spaces of maps into finite-dimensional Symmetrie spaces, and this description gives our spaces attractive geometric properties, such äs curvatures which are computable for certain mapping functors by the methods of the appendix to [FG]. The groups of maps considered here may be viewed äs the Ä-points of a linear algebraic group, where R is a subring of the coordinate ring of an affine variety, and this paper offers a characterization of a good class of rings R

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1993

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