Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.

Keywords:

resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedron resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedron

MSC Classifications:

18G10, 05C05, 16S10, 17B01, 17A50, 18G50 show english descriptions Resolutions; derived functors [See also 13D02, 16E05, 18E25]
Trees
Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
Identities, free Lie (super)algebras
Free algebras
Nonabelian homological algebra 18G10 - Resolutions; derived functors [See also 13D02, 16E05, 18E25]
05C05 - Trees
16S10 - Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
17B01 - Identities, free Lie (super)algebras
17A50 - Free algebras
18G50 - Nonabelian homological algebra

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