Archiv der Mathematik

, Volume 70, Issue 3, pp 187–196 | Cite as

Primeness of the enveloping algebra of the special Lie superalgebras

  • Mark C. Wilson
  • Geoffrey Pritchard

Abstract.

A primeness criterion due to Bell is shown to apply to the universal enveloping algebra of the Cartan type Lie superalgebras S (V ) and \( \widetilde {S}(V;t) \) when dim V is even. This together with other recent papers yields¶¶Theorem. Let L be a finite-dimensional simple Lie superalgebra over an algebraically closed field of characteristic zero. Then L satisfies Bell's criterion (so that U ( L) is prime and hence semiprimitive), unless L is of one of the types: b (n) for n≥ 3; W (n) for odd n≥ 5; S (n) for odd n≥ 3.¶¶ On the other hand, if dim V is odd then U (S(V )) is never semiprime.

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Mark C. Wilson
    • 1
  • Geoffrey Pritchard
    • 2
  1. 1.Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New ZealandNZ
  2. 2.Department of Mathematics, Texas A & M University, College Station, TX 77843, USAUS
  3. 3.Current address: Department of Statistics, University of Auckland, Private Bag 92019 Auckland, New ZealandNZ

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