I am confused of definition of Free Lie sum and Free product of Lie algebras? May you please give some examples and an explicit definition of them?
2026-03-25 17:53:00.1774461180
Free Lie sum vs free Lie product
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The free Lie sum, or the free product of Lie algebras is defined, for example, here, in section $6$, Definition $6.4$, as ususal with a universal property. It is denoted by $L_1\ast L_2$. Shirshov has given the first linear basis for the free product of Lie algebras.