Cohomology of Lie -groups

  • Grégory Ginot

    Université Pierre et Marie Curie, Paris, France
  • Ping Xu

    University of Luxembourg, Luxembourg


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