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Central Elements in the Universal Enveloping Algebras for the Split Realization of the Orthogonal Lie Algebras

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Abstract

We construct central elements in the universal enveloping algebra using column-determinants for the split realization of the orthogonal Lie algebra. Our central elements are quite new and simple, though they are closely related to what Howe and Umeda gave for the orthogonal Lie algebra under the different realization as the alternating matrices.

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  1. Division of Comprehensive Education, Hokkaido Institute of Technology, Sapporo, 006-8585, Japan

    Akihito Wachi

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  1. Akihito Wachi
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Correspondence to Akihito Wachi.

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Wachi, A. Central Elements in the Universal Enveloping Algebras for the Split Realization of the Orthogonal Lie Algebras. Lett Math Phys 77, 155–168 (2006). https://doi.org/10.1007/s11005-006-0082-6

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  • DOI: https://doi.org/10.1007/s11005-006-0082-6

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