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Combinatorial and group-theoretic compactifications of buildings

Pierre-Emmanuel Caprace, Jean Lécureux (2011)

Annales de l’institut Fourier

Let X be a building of arbitrary type. A compactification 𝒞 sph ( X ) of the set Res sph ( X ) of spherical residues of X is introduced. We prove that it coincides with the horofunction compactification of Res sph ( X ) endowed with a natural combinatorial distance which we call the root-distance. Points of 𝒞 sph ( X ) admit amenable stabilisers in Aut ( X ) and conversely, any amenable subgroup virtually fixes a point in 𝒞 sph ( X ) . In addition, it is shown that, provided Aut ( X ) is transitive enough, this compactification also coincides with the group-theoretic...

Hopf algebras of smooth functions on compact Lie groups

Eva C. Farkas (2000)

Commentationes Mathematicae Universitatis Carolinae

A C -Hopf algebra is a C -algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C -Hopf algebras which are given by the algebra C ( G ) of smooth functions on some compact Lie group G , thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

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