Spectral triples for finitely generated groups, index 0.

Sébastien Palcoux (1)

1 IML - Institut de mathématiques de Luminy

Using Cayley graphs and Clifford algebras, we are able to give, for every finitely generated groups, a uniform construction of spectral triples with a generically non-trivial phase for the Dirac operator. Unfortunatly $D_{+}$ is index $0$, but we are naturally led to an interesting classification of finitely generated groups into three types.

Mots clés: non-commutative geometry; spectral triple; geometric group theory; Clifford algebra; Cayley graph; Dirac; finitely generated group

Domaines: Algèbres d'opérateurs [math.OA]

Sébastien Palcoux. Spectral triples for finitely generated groups, index 0.. 2010. ⟨hal-00529553v8⟩