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

Naoya Suzuki

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arXiv · 1310.4559

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

Naoya Suzuki

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Abstract

When a Lie group $G$ has a central $U(1)$-extension, there is a cocycle in the simplicial de Rham complex $\Omega^3(NG)$ which represents the Dixmier-Douady class. Mickelsson and Brylinski, McLaughlin constructed a central $U(1)$-extension $\widehat{LSU(2)} \rightarrow LSU(2)$ whose Dixmier-Douady class in $\Omega^3(NLSU(2))$ is a kind of transgression of the second Chern class. In this paper, we consider the case of unitary group and construct a central $U(1)$-extension of $LU(2)$. After that we construct also a cocycle in a certain triple complex.

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BibTeX RIS

Naoya Suzuki. 2013-10-17. On some cocycles which represent the Dixmier-Douady class in simplicial de Rham complexes. https://arxiv.org/abs/1310.4559

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