Letters in Mathematical Physics

, Volume 66, Issue 1–2, pp 141–155 | Cite as

Back to the Amitsur–Levitzki Theorem: a Super Version for the Orthosymplectic Lie Superalgebra \({\mathfrak{o}}{\mathfrak{s}}{\mathfrak{p}}\left( {1,2n} \right)\)

  • P-A. Gié
  • G. Pinczon
  • R. Ushirobira
Article

Abstract

We prove an Amitsur–Levitzki type theorem for the Lie superalgebras \(\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)\)) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras \(\mathfrak{g}\mathfrak{l}\left( {p,q} \right)\) cannot satisfy an Amitsur–Levitzki type super identity if pq≠0 and conjecture that neither can any other classical simple Lie superalgebra with the exception of \(\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)\).

Amitsur–Levitzki theorem Lie superalgebras transgression operator 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • P-A. Gié
    • 1
  • G. Pinczon
    • 1
  • R. Ushirobira
    • 1
  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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