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math.OA2003★ 18 cited
L^2-Homology for von Neumann Algebras
Alain Connes, Dimitri Shlyakhtenko
We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these i…
math.QA2003★ 4 cited
Rankin-Cohen Brackets and the Hopf Algebra of Transverse Geometry
Alain Connes, Henri Moscovici
We settle in this paper a question left open in our paper ``Modular Hecke algebras and their Hopf symmetry'', by showing how to extend the Rankin-Cohen brackets from modular forms…
math.QA2003★ 9 cited
Modular Hecke Algebras and their Hopf Symmetry
Alain Connes, Henri Moscovici
We introduce and begin to analyse a class of algebras, associated to congruence subgroups, that extend both the algebra of modular forms of all levels and the ring of classical Hec…