Rational discrete cohomology and homology for a totally disconnected locally compact group G are introduced and studied. The Hom-⊗ identity associated to the rational discrete bimodule Bi(. G) allows to introduce the notion of rational duality group in analogy to the discrete case. It is shown that a semi-simple algebraic group G(. K) defined over a non-discrete, non-archimedean local field K is a rational t.d.l.c. duality group, and the same is true for certain topological Kac-Moody groups. Indeed, for these groups the Tits (or Davis) realization of the associated building is a finite-dimensional model of the classifying space E_C(G(K)) one may define for any t.d.l.c. group. In contrast, Y. Neretin's group of spheromorphisms of a locally finite regular tree is not even of finite rational discrete cohomological dimension.

Castellano, I., Weigel, T. (2016). Rational discrete cohomology for totally disconnected locally compact groups. JOURNAL OF ALGEBRA, 453, 101-159 [10.1016/j.jalgebra.2016.01.008].

Rational discrete cohomology for totally disconnected locally compact groups

CASTELLANO, ILARIA
;
WEIGEL, THOMAS STEFAN
2016

Abstract

Rational discrete cohomology and homology for a totally disconnected locally compact group G are introduced and studied. The Hom-⊗ identity associated to the rational discrete bimodule Bi(. G) allows to introduce the notion of rational duality group in analogy to the discrete case. It is shown that a semi-simple algebraic group G(. K) defined over a non-discrete, non-archimedean local field K is a rational t.d.l.c. duality group, and the same is true for certain topological Kac-Moody groups. Indeed, for these groups the Tits (or Davis) realization of the associated building is a finite-dimensional model of the classifying space E_C(G(K)) one may define for any t.d.l.c. group. In contrast, Y. Neretin's group of spheromorphisms of a locally finite regular tree is not even of finite rational discrete cohomological dimension.
Articolo in rivista - Articolo scientifico
Rational discrete cohomology, totally disconnected locally compact groups
English
101
159
59
Castellano, I., Weigel, T. (2016). Rational discrete cohomology for totally disconnected locally compact groups. JOURNAL OF ALGEBRA, 453, 101-159 [10.1016/j.jalgebra.2016.01.008].
Castellano, I; Weigel, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/139075
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