Free group $C^*$-algebras associated with $\ell_p$

Details Free group $C^*$-algebras associated with $\ell_p$ Free group $C^*$-algebras associated with $\ell_p$

2012-03-05

arxiv.org/abs/1203.0800v1

Mathematics

Operator Algebras

Scientific paper

For every $p\geq 2$, we give a characterization of positive definite
functions on a free group with finitely many generators, which can be extended
to the positive linear functionals on the free group $C^*$-algebra associated
with the ideal $\ell_p$. As a consequence, the associated $C^*$-algebras are
mutually non-isomorphic, and they have a unique tracial state.

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