$B^p_r(F_n)$ has no nontrivial idempotents

preprint2022arXivOpen access

We show that there is no nontrivial idempotent in the reduced group $\ell^p$ -operator algebra $B^p_r(F_n)$ of the free group $F_n$ on $n$ generators for each positive integer $n$ .

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$B^p_r(F_n)$ has no nontrivial idempotents

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Brp(Fn)B^p_r(F_n)Brp​(Fn​) has no nontrivial idempotents

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$B^p_r(F_n)$ has no nontrivial idempotents