A note on the Chevalley–Eilenberg cohomology for the Galilei and Poincaré algebras

2008/08/31 by Sotirios Bonanos, Joaquim Gomis · 2 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Cohomology #Construct (python library) #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #Poincaré conjecture #Symmetry (geometry) #Symmetry group #hep-th

paper · pdf · doi:10.1088/1751-8113/42/14/145206

published as J.Phys.A42:145206,2009 · 11 pages, no figures Added several references, corrected typos

arxiv created 2009/03/03 · openalex publication_date 2009/03/16 · arxiv updated 2011/06/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We construct in a systematic way the complete Chevalley–Eilenberg cohomology at form degrees 2, 3 and 4 for the Galilei and Poincaré groups. The corresponding non-trivial forms belong to certain representations of the spatial rotation (Lorentz) group. In the case of 2-forms they give all possible central and non-central extensions of the Galilei group (and all non-central extensions of the Poincaré group). The procedure developed in this paper can be applied to any spacetime symmetry group.

Citations

• Tensor extension of the Poincaré algebra
• Nonrelativistic closed string theory
• IIA/B, wound and wrapped
• Structure of Phenomenological Lagrangians. I
• On Unitary Ray Representations of Continuous Groups
• Structure of Phenomenological Lagrangians. II
• Possible Kinematics

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