Finite Gröbner-Shirshov bases are constructed in Lee algebras, suggesting new representation methods for these structures.
It is shown that every Lee algebra of finite rank admits a finite Gröbner-Shirshov basis, which is proved by constructing a finite complete rewriting system for the corresponding Lee monoid [Formula: see text] for each [Formula: see text]. Further, we explicitly construct a faithful representation for each [Formula: see text], and this faithful representation can be extended to the involution case.
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Luo et al. (2026) studied this question.
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