A few remarks on Pimsner–Popa bases and regular subfactors of depth 2
We prove that a finite index regular inclusion of-factors with commutative first relative
commutant is always a crossed product subfactor with respect to a minimal action of a
biconnected weak Kac algebra. Prior to this, we prove that every finite index inclusion of-
factors which is of depth 2 and has simple first relative commutant (respectively, is regular
and has commutative or simple first relative commutant) admits a two-sided Pimsner–Popa
basis (respectively, a unitary orthonormal basis).
commutant is always a crossed product subfactor with respect to a minimal action of a
biconnected weak Kac algebra. Prior to this, we prove that every finite index inclusion of-
factors which is of depth 2 and has simple first relative commutant (respectively, is regular
and has commutative or simple first relative commutant) admits a two-sided Pimsner–Popa
basis (respectively, a unitary orthonormal basis).
We prove that a finite index regular inclusion of -factors with commutative first relative commutant is always a crossed product subfactor with respect to a minimal action of a biconnected weak Kac algebra. Prior to this, we prove that every finite index inclusion of -factors which is of depth 2 and has simple first relative commutant (respectively, is regular and has commutative or simple first relative commutant) admits a two-sided Pimsner–Popa basis (respectively, a unitary orthonormal basis).
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