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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Involutory automorphisms of operator algebras


Author: E. B. Davies
Journal: Trans. Amer. Math. Soc. 158 (1971), 115-142
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9947-1971-0284818-0
MathSciNet review: 0284818
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Abstract: We develop the mathematical machinery necessary in order to describe systematically the commutation and anticommutation relations of the field algebras of an algebraic quantum field theory of the fermion type. In this context it is possible to construct a skew tensor product of two von Neumann algebras and completely describe its type in terms of the types of the constituent algebras. Mathematically the paper is a study of involutory automorphisms of $ {W^\ast}$-algebras, of particular importance to quantum field theory being the outer involutory automorphisms of the type III factors. It is shown that each of the hyperfinite type III factors studied by Powers has at least two outer involutory automorphisms not conjugate under the group of all automorphisms of the factor.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0284818-0
Keywords: $ {C^\ast}$-aIgebras, involutory automorphisms, anticommutation relations, hyperfinite von Neumann algebras
Article copyright: © Copyright 1971 American Mathematical Society