When Hom-Lie structures form a Jordan algebra

Abstract

We are concerned with the question when Hom-Lie structures on a Lie algebra are closed with respect to the Jordan product. Somewhat unexpectedly, this leads us to certain questions connected with the Yang-Baxter equation, and with decomposition of a Lie algebra into the sum of subalgebras with given properties.

8 pages; for the latest version of this text, see https://web.osu.cz/~Zusmanovich/papers/