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On Central Elements in the Universal Enveloping Algebras of the Orthogonal Lie Algebras

  • Minoru Itoh (a1) and Tôru Umeda (a1)
  • DOI: http://dx.doi.org/10.1023/A:1017571403369
  • Published online: 01 July 2001
Abstract

We present an analogy of the famous formula that the square of the Pfaffian is equal to the determinant for an alternating matrix for the case where the entries are the generators of the orthogonal Lie algebras. This identity clarifies the relation between the two sets of central elements in the enveloping algebra of the orthogonal Lie algebras. We employ systematically the exterior calculus for the proof.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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