On some cocycles which represent the Dixmier-Douady class in simplicial de Rham complexes

Naoya Suzuki

Published 2013-10-17, updated 2015-03-18Version 13

There is a cocycle in the simplicial de Rham complex which represents the Dixmier-Douady class. We explain that this cocycle coincides with a kind of transgression of the second Chern class when we consider a central extension of the loop group and a connection form due to J. Mickelsson and J-L. Brylinski, D. McLaughlin. After that we construct also a cocycle in a certain triple complex. Furthermore, we explain the relationship between our cocycle and the another description of the Dixmier-Douady class due to K. Behrend and P. Xu.