Characteristic Classes

Victor W. Guillemin, Shlomo Sternberg and Jochen Brüning
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Victor W. Guillemin: Massachusetts Institute of Technology, Department of Mathematics
Shlomo Sternberg: Harvard University, Department of Mathematics
Jochen Brüning: Humboldt-Universität Berlin, Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät II

Chapter Chapter 8 in Supersymmetry and Equivariant de Rham Theory, 1999, pp 95-110 from Springer

Abstract: Abstract Recall from section 4.5 that if A is a G* module, then we have a characteristic homomorphism $${k_*}:S{({g^*})^G} \to {H_G}(A),$$ and that the elements of the image of k * are known as characteristic classes. But we have not really written down what the ring S (g*) G is for any group G. The main function of this chapter is to remedy this by summarizing standard computations of S (g*) G for various important groups. Suppose that: ø : K → G is a Lie group homomorphism, and let k denote the Lie algebra of K. The induced Lie algebra map k → g dualizes to a map g* → k* which extends to an algebra homomorphism S(g*)G → S(k*)k. We will examine this homomorphism for various examples of inclusions of classical groups.

Keywords: Vector Bundle; Line Bundle; Characteristic Classis; Complex Vector Space; Cartan Subgroup (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-3-662-03992-2_8

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