A homotopy construction of the adjoint representation for Lie groups. (English) Zbl 1027.55015

Castellana, Natàlia; Kitchloo, Nitu

Math. Proc. Camb. Philos. Soc. 133, No. 3, 399-409 (2002).

From the authors’ abstract: Let \(G\) be a compact, simply-connected, simple Lie group and \(T\subset G\) a maximal torus. The purpose of this paper is to study the connection between various fibrations over \(BG\) (where \(G\) is a compact, simply-connected, simple Lie group) associated to the adjoint representation and homotopy colimits over poset categories \(\mathcal C\), \(\text{hocolim}_\mathcal C\) \(BG_I\) where \(G_I\) are certain connected maximal rank subgroups of \(G\).

Reviewer: M.Mimura (Okayama)

MSC:

55R20	Spectral sequences and homology of fiber spaces in algebraic topology
57T99	Homology and homotopy of topological groups and related structures
55R40	Homology of classifying spaces and characteristic classes in algebraic topology

Keywords:

Lie groups; adjoint representation