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L²-homology and reciprocity for right-angled Coxeter groups

Boris Okun, Richard Scott (2011)

Fundamenta Mathematicae

Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra μ containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define L ² μ -Betti numbers and an L ² μ -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version of Poincaré...

La décomposition en poids des algèbres de Hopf

Frédéric Patras (1993)

Annales de l'institut Fourier

Si H est une algèbre de Hopf commutative ou cocommutative et connexe, les puissances de convolution Ψ k et le logarithme, au sens du produit de convolution, du morphisme identité de H satisfont à diverses identités algébriques. L’algèbre de Hopf H admet en particulier une décomposition en poids sous l’action des morphismes Ψ k , dont nous étudions les propriétés.

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