Chern-Simons Classes and Cocycles on the Lie Algebra of the Gauge Group
Identifieur interne : 001B15 ( Main/Exploration ); précédent : 001B14; suivant : 001B16Chern-Simons Classes and Cocycles on the Lie Algebra of the Gauge Group
Auteurs : I. M. Gelfand [États-Unis] ; M. M. Smirnov [Allemagne, États-Unis]Source :
Abstract
Abstract: We consider here generalizations of Chern-Simons classes and related algebraic problems. We describe a new class of algebras whose elements contain Chern and generalized Chern-Simons classes. There is a Poisson bracket in these algebras similar to [Kon]. Using this bracket we construct a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. We develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action. At the end we give new explicit formulas for cocycles on a gauge group and for corresponding cocycles on the Lie algebra constructed using our explicit formulas for generalized Chern-Simons classes given in the Appendix.
Url:
DOI: 10.1007/978-1-4612-4082-2_7
Affiliations:
- Allemagne, États-Unis
- New Jersey, État de New York
- New Brunswick (New Jersey), New York
- Université Columbia, Université Rutgers
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M." last="Gelfand">I. M. Gelfand</name><affiliation wicri:level="4"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Dept. of Math., Rutgers University, 08903, New Brunswick, NJ</wicri:regionArea><placeName><region type="state">New Jersey</region><settlement type="city">New Brunswick (New Jersey)</settlement></placeName><orgName type="university">Université Rutgers</orgName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author><author><name sortKey="Smirnov, M M" sort="Smirnov, M M" uniqKey="Smirnov M" first="M. M." last="Smirnov">M. M. Smirnov</name><affiliation wicri:level="1"><country xml:lang="fr">Allemagne</country><wicri:regionArea>Max-Planck Institut für Mathematik Bonn, Germany and Princeton University</wicri:regionArea><wicri:noRegion>Germany and Princeton University</wicri:noRegion><wicri:noRegion>Germany and Princeton University</wicri:noRegion></affiliation><affiliation wicri:level="4"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Columbia University, NY</wicri:regionArea><placeName><region type="state">État de New York</region><settlement type="city">New York</settlement></placeName><orgName type="university">Université Columbia</orgName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author></analytic><monogr></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We consider here generalizations of Chern-Simons classes and related algebraic problems. We describe a new class of algebras whose elements contain Chern and generalized Chern-Simons classes. There is a Poisson bracket in these algebras similar to [Kon]. Using this bracket we construct a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. We develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action. At the end we give new explicit formulas for cocycles on a gauge group and for corresponding cocycles on the Lie algebra constructed using our explicit formulas for generalized Chern-Simons classes given in the Appendix.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>États-Unis</li></country><region><li>New Jersey</li><li>État de New York</li></region><settlement><li>New Brunswick (New Jersey)</li><li>New York</li></settlement><orgName><li>Université Columbia</li><li>Université Rutgers</li></orgName></list><tree><country name="États-Unis"><region name="New Jersey"><name sortKey="Gelfand, I M" sort="Gelfand, I M" uniqKey="Gelfand I" first="I. M." last="Gelfand">I. M. Gelfand</name></region><name sortKey="Gelfand, I M" sort="Gelfand, I M" uniqKey="Gelfand I" first="I. M." last="Gelfand">I. M. Gelfand</name><name sortKey="Smirnov, M M" sort="Smirnov, M M" uniqKey="Smirnov M" first="M. M." last="Smirnov">M. M. Smirnov</name><name sortKey="Smirnov, M M" sort="Smirnov, M M" uniqKey="Smirnov M" first="M. M." last="Smirnov">M. M. Smirnov</name></country><country name="Allemagne"><noRegion><name sortKey="Smirnov, M M" sort="Smirnov, M M" uniqKey="Smirnov M" first="M. M." last="Smirnov">M. M. Smirnov</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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