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Le complexe de Koszul en algèbre et topologie

Stephen Halperin (1987)

Annales de l'institut Fourier

The Koszul complex, as introduced in 1950, was a differential graded algebra which modelled a principal fibre bundle. Since then it has been an effective tool, both in algebra and in topology, for the calculation of homological and homotopical invariants. After a partial summary of these results we recall more recent generalizations of this complex, and some applications.

Left-right noncommutative Poisson algebras

José Casas, Tamar Datuashvili, Manuel Ladra (2014)

Open Mathematics

The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as...

Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras

Johannes Huebschmann (1998)

Annales de l'institut Fourier

For any Lie-Rinehart algebra ( A , L ) , B(atalin)-V(ilkovisky) algebra structures on the exterior A -algebra Λ A L correspond bijectively to right ( A , L ) -module structures on A ; likewise, generators for the Gerstenhaber algebra Λ A L correspond bijectively to right ( A , L ) -connections on A . When L is projective as an A -module, given a B-V algebra structure on Λ A L , the homology of the B-V algebra ( Λ A L , ) coincides with the homology of L with coefficients in A with reference to the right ( A , L ) -module structure determined by . When...

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