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An example of a simple double Lie algebra. (English) Zbl 1511.17042

Summary: We extend the correspondence between double Lie algebras and skew-symmetric Rota-Baxter operators of weight 0 on the matrix algebra to the infinite-dimensional case. We give the first example of a simple double Lie algebra.

MSC:

17B38 Yang-Baxter equations and Rota-Baxter operators
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16W99 Associative rings and algebras with additional structure
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References:

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