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.
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Gelfand, I.M., Smirnov, M.M. (1996). Chern-Simons Classes and Cocycles on the Lie Algebra of the Gauge Group. In: Gelfand, I.M., Lepowsky, J., Smirnov, M.M. (eds) The Gelfand Mathematical Seminars, 1993–1995. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4082-2_7
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DOI: https://doi.org/10.1007/978-1-4612-4082-2_7
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