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