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Inner equivalence of thick subalgebras Kerr, Charles R.

Abstract

In this thesis we construct some examples of thick subalgebras ɛ of factors ɑ. ɛ is thick in ɑ if (ɛ' ∩ ɑ) is maximal abelian in ɑ. We are concerned with their inner equivalence: given the thick subalgebras ɛ and ℱ in ɑ, does there exist a unitary U є ɑ such that U є U* = ℱ ? Examples of thick subalgebras which are not maximal abelian have been given by Dixmier and Kadison. Later Bures constructed numerous examples which he distinguished by use of certain invariants. We use Bures's construction to get, in certain factors ɑ of types II₁,- II₀₀, III, uncountable families {ɛ[subscript i]: iєℱ} of thick subalgebras of ɑ such that ɛ[subscript i] is not inner equivalent to ɛ[subscript J] when i ≠ J (We are able to add one example to those constructed by Bures). In each family, the ɛ[subscript i]cannot be distinguished by means of Bures's invariants, and so we are forced to show their non-inner-equivalence by direct calculations.

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