Cohomology of Lie -groups
Grégory Ginot
Université Pierre et Marie Curie, Paris, FrancePing Xu
University of Luxembourg, Luxembourg
![Cohomology of Lie $2$-groups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-lem-volume-55-issue-3.png&w=3840&q=90)
Abstract
We study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott–Shulman type map in the case of a Lie 2-group corresponding to the crossed module . The cohomology of the Lie 2-groups corresponding to the universal crossed modules and is the abutment of a spectral sequence involving the cohomology of and . When the dimension of the center of is less than 3, we compute these cohomology groups explicitly. We also compute the cohomology of the Lie 2-group corresponding to a crossed module for which is compact and Coker is connected, simply connected and compact, and we apply the result to the string 2-group.
Cite this article
Grégory Ginot, Ping Xu, Cohomology of Lie -groups. Enseign. Math. 55 (2009), no. 3/4, pp. 373–396
DOI 10.4171/LEM/55-3-8