If L be lie algebra over F ( F is a field), I want to know what is the definition of absolutely irreducible FL-module? I have confused of several key words related to irreducible modules!? Is there any difference between completely irreducible and absolutely irreducible?
2026-04-03 14:13:50.1775225630
absolutely irreducible module
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When I google "absolutely irreducible module" the second hit I get is a passage in Lam's Exercises in classical ring theory which explains that an irreducible module $M$ over a $k$ algebra $R$ ($k$ a field) is called absolutely irreducible if $M\otimes_k K$ is irreducible over $R\otimes_k K$ for every extension field K of k.
I would guess the FL part is a semigroup algebra... Hard to tell without more context.
It is commonplace for definitions of modules for associative rings are re-used (where applicable) for modules over Lie algebras. For example, "irreducible module" is used here to mean a module with only trivial modules no matter if the algebra is associative or if it is Lie. So it seems it would use the same definition for Lie modules.