The Roots of Exceptional Modular Lie Superalgebras with Cartan Matrix

Sofiane Bouarroudj, Dimitry Leites, Olexander Lozhechnyk, Jin Shang

Research output: Contribution to journalArticlepeer-review

Abstract

For each of the exceptional (not entering infinite series) finite-dimensional modular Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots, and the corresponding Chevalley basis, for one of its inequivalent Cartan matrices, namely the one corresponding to the greatest number of mutually orthogonal isotropic odd simple roots (this number, called the defect of the Lie superalgebra, is important in the representation theory). Our main tools: Grozman’s Mathematica-based code SuperLie, Python, and A. Lebedev’s help.

Original languageEnglish (US)
Pages (from-to)63-118
Number of pages56
JournalArnold Mathematical Journal
Volume6
Issue number1
DOIs
StatePublished - Mar 1 2020

Keywords

  • Cartan matrix
  • Modular Lie superalgebra

ASJC Scopus subject areas

  • Mathematics(all)

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