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Three Schur functors related to pre-Lie algebras

DOTSENKO, VLADIMIR ; FLYNN-CONNOLLY, OISÍN

Mathematical proceedings of the Cambridge Philosophical Society, 2024-03, Vol.176 (2), p.441-458 [Periódico revisado por pares]

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Título:
Three Schur functors related to pre-Lie algebras
Autor: DOTSENKO, VLADIMIR ; FLYNN-CONNOLLY, OISÍN
Assuntos: Algebra ; Combinatorial analysis ; Combinatorics ; Descriptions ; Homology ; Lie groups ; Modules ; Theorems ; Vector space ; Vector spaces ; Vectors (mathematics)
É parte de: Mathematical proceedings of the Cambridge Philosophical Society, 2024-03, Vol.176 (2), p.441-458
Descrição: We give explicit combinatorial descriptions of three Schur functors arising in the theory of pre-Lie algebras. The first of them leads to a functorial description of the underlying vector space of the universal enveloping pre-Lie algebra of a given Lie algebra, strengthening the Poincaré-Birkhoff-Witt (PBW) theorem of Segal. The two other Schur functors provide functorial descriptions of the underlying vector spaces of the universal multiplicative enveloping algebra and of the module of Kähler differentials of a given pre-Lie algebra. An important consequence of such descriptions is an interpretation of the cohomology of a pre-Lie algebra with coefficients in a module as a derived functor for the category of modules over the universal multiplicative enveloping algebra.
Editor: Cambridge, UK: Cambridge University Press
Idioma: Inglês

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