Abstract
Wendel showed that norm non-increasing isomorphisms between the group algebras of locally compact groups could be expressed in terms of group characters and topological isomorphisms. His results are extended to twisted group algebras. In particular, by applying a generalisation ofWendel's main result to twisted group algebras over the same group, it is shown that the number of such algebras is equal to the number of orbits in a 2-cohomology group overG under the action of the automorphism group ofG. An application to the twisted group algebra defined byWeyl's form of the canonical commutation relations is considered.
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References
Bargmann, V.: On unitary ray representations of continuous groups. Ann. Math. 59, 1–46 (1954).
Dixmler, J.: Les C*-algebras and leurs representations. Paris: Gauthiers-Villars 1964.
Edwards, C. M.: Twisted group algebras and their representations. Oxford D. Phil. Thesis (1966).
——, andJ. T. Lewis: Twisted group algebras I. Commun. math. Phys.13, 119–130 (1969).
Hewitt, E., andK. A. Ross: Abstract harmonic analysis I. Berlin-Göttingen-Heidelberg: Springer 1963.
Hochschild, G.: Group extensions of Lie groups I, Ann. Math.54, 96–109 (1951).
von Neumann, J.: Die Eindeutigkeit der Schrödingerschen Operatoren. Math. Ann.104, 570–578 (1931).
Wendel, J. G.: Left centralisers and isomorphisms of group algebras. Pacific J. Math.2, 251–261 (1952).
Weyl, H.: Theory of groups and quantum mechanics. London: Dover 1931.
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Edwards, C.M., Lewis, J.T. Twisted group algebras II. Commun.Math. Phys. 13, 131–141 (1969). https://doi.org/10.1007/BF01649872
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DOI: https://doi.org/10.1007/BF01649872