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Left invariant poisson structures on classical non-compact simple Lie groups

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Abstract

A Poisson structure on a Lie group is called left invariant if the contravariant 2-tensor field π corresponding to the Poisson structure is left invariant. Explicit examples of such structures were known only for few cases, and in this paper, we give new examples of high rank left invariant Poisson structures for all non-compact classical real simple Lie groups. This result is equivalent to give constant solutions of the classical Yang-Baxter equation [r 12,r 13]+[r 12,r 23]+[r 13,r 23]=0 taking values in the space ^2g for these Lie groups.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Integrated Arts and Sciences, Hiroshima University, 739-8521, Higashi-Hiroshima, Japan

    Yoshio Agaoka

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  1. Yoshio Agaoka
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Correspondence to Yoshio Agaoka.

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Agaoka, Y. Left invariant poisson structures on classical non-compact simple Lie groups. Isr. J. Math. 116, 189–222 (2000). https://doi.org/10.1007/BF02773218

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  • DOI: https://doi.org/10.1007/BF02773218

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