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

Published online by Cambridge University Press:  04 December 2007

Minoru Itoh  and
Tôru Umeda
Minoru Itoh
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan
Tôru Umeda
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan
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Abstract

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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.

Keywords

center of universal enveloping algebraorthogonal Lie algebra
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 3 , July 2001 , pp. 333 - 359
Copyright
© 2001 Kluwer Academic Publishers