Abstract
In this paper, we initiate the study of C *-algebras endowed with a twisted action of a locally compact abelian Lie group , and we construct a twisted crossed product , which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to T-duality in Type II string theory to obtain the T-dual of a general principal torus bundle with general H-flux, which we will argue to be a bundle of noncommutative, nonassociative tori. Nonassociativity is interpreted in the context of monoidal categories of modules. We also show that this construction of the T-dual includes the other special cases already analysed in a series of papers.
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Communicated by M.R. Douglas
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Bouwknegt, P., Hannabuss, K. & Mathai, V. Nonassociative Tori and Applications to T-Duality. Commun. Math. Phys. 264, 41–69 (2006). https://doi.org/10.1007/s00220-005-1501-8
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DOI: https://doi.org/10.1007/s00220-005-1501-8