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Double Lie algebras of a nonzero weight (2104.13678v2)

Published 28 Apr 2021 in math.RA

Abstract: We introduce the notion of $\lambda$-double Lie algebra, which coincides with usual double Lie algebra when $\lambda = 0$. We state that every $\lambda$-double Lie algebra for $\lambda\neq0$ provides the structure of modified double Poisson algebra on the free associative algebra. In particular, it confirms the conjecture of S. Arthamonov (2017). We prove that there are no simple finite-dimensional $\lambda$-double Lie algebras.

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