99-264 Jan Naudts

C*-multipliers, crossed product algebras, and canonical commutation relations. (49K, latex) Jul 12, 99

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Abstract. The notion of a multiplier of a group X is generalized to that of a C*-multiplier by allowing it to have values in an arbitrary C*-algebra A. On the other hand, the construction of the crossed product algebra A x X is generalized by replacing the action of X in A by a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. The generalizations are done in such a way that a one-to-one correspondence exists between C*-multipliers and projective actions. The results are applicable in mathematical physics. Quantum spacetime is discussed as an example.

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