On Central Elements in the Universal Enveloping Algebras of the Orthogonal Lie Algebras |
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Authors: | Minoru Itoh Tôru Umeda |
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Institution: | (1) Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606, Japan |
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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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Keywords: | center of universal enveloping algebra orthogonal Lie algebra |
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