Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toeplitz CAR flows and type I factorizations   Toeplitz CAR flows are a class of E_0-semigroups including the first type III
example constructed by R. T. Powers. We show that the Toeplitz CAR flows
contain uncountably many mutually non cocycle conjugate E_0-semigroups of type
III. We also generalize the type III criterion for Toeplitz CAR flows employed
by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows
are always either of type I or type III.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat