2007/08/31 by Brian D. Boe, Jonathan R. Kujawa, Daniel K. Nakano · 30 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Mathematics #Pure mathematics #math.RT #msc:17B10 #msc:17B56
paper · pdf · doi:10.1112/plms/pdn019
published in Proceedings of the London Mathematical Society 98(1), 19-44 (Wiley) · 28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixed
arxiv created 2007/11/20 · openalex publication_date 2008/05/02 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In [2] (Preprint, 2006, arXiv:math.RT/0609363) the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra, and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties of Kac supermodules for Type-I Lie superalgebras and of the simple supermodules for g l(m|n). The latter result verifies our earlier conjecture for g l(m|n). In our investigation we also delineate several of the major differences between Type-I versus Type-II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.