1999/07/09 by Jan Naudts, Naudts, Jan
Mathematics · Physics and Astronomy · #22d25 #46l60 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA #msc:22d25 #msc:46l60
paper · pdf · doi:10.48550/arxiv.math-ph/9907008
slightly improved version, 26 pages (originally 21)
arxiv created 2000/03/20 · arxiv updated 2009/11/30
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 notion of the action of X in A is generalized to that of a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. It is shown that there exists a one-to-one correspondence between C*-multipliers and projective actions. C*-multipliers have been used to define twisted group algebras. On the other hand, the projective action tau can be used to construct the crossed product algebra A xtau X. Both constructions are unified in the present approach. The results are applicable in mathematical physics. The multiplier algebra of the crossed product algebra A xtau X contains Weyl operators W(x),x in X. They satisfy canonical commutation relations w.r.t. the C*-multiplier. Quantum spacetime is discussed as an example.