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

2013/10/17 by Naoya Suzuki, Suzuki, Naoya
Mathematics · #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG

paper · pdf · doi:10.48550/arxiv.1310.4559

15 pages

openalex publication_date 2013/10/17 · openalex created_date 2016/07/22 · arxiv created 2018/07/08 · arxiv updated 2018/07/10 · openalex updated_date 2026/07/28

Abstract

When a Lie group G has a central U(1)-extension, there is a cocycle in the simplicial de Rham complex Ω³(NG) which represents the Dixmier-Douady class. Mickelsson and Brylinski, McLaughlin constructed a central U(1)-extension \widehatLSU(2) → LSU(2) whose Dixmier-Douady class in Ω³(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.

Related

• The Dixmier-Douady class in the Simplicial de Rham Complex
• A central U(1)-extension of a double Lie groupoid
• The Euler class in the Simplicial de Rham Complex
• The Chern Character in the Simplicial de Rham Complex
• Simplicial Hochschild cochains as an Amitsur complex