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Homologie et modèle minimal des algèbres de Gerstenhaber

Grégory Ginot (2004)

Annales mathématiques Blaise Pascal

On étudie ici les notions d’algèbre de Gerstenhaber à homotopie près et d’homologie des algèbres de Gerstenhaber du point de vue de la théorie des opérades. Précisément, on donne une description explicite des 𝒢 -algèbres à homotopie près (c’est-à-dire d’algèbres sur le modèle minimal de l’opérade 𝒢 des algèbres de Gerstenhaber). On décrit également le complexe calculant l’homologie des 𝒢 -algèbres. On donne une suite spectrale qui converge vers cette homologie et quelques exemples de calculs. Enfin...

Homology and cohomology of Rees semigroup algebras

Frédéric Gourdeau, Niels Grønbæk, Michael C. White (2011)

Studia Mathematica

Let S be a Rees semigroup, and let ℓ¹(S) be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of ℓ¹(S) are isomorphic to those of the underlying discrete group algebra.

Homotopy representability of Brauer groups.

Antonio Martínez Cegarra (1999)

Extracta Mathematicae

The purpose of this paper is to present certain facts and results showing a way through which simplicial homotopy theory can be used in the study of Auslander-Goldman-Brauer groups of Azumaya algebras over commutative rings.

Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs

Dennis Sullivan (2009)

Banach Center Publications

Using the algebraic theory of homotopies between maps of dga's we obtain a homotopy theory for algebraic structures defined by collections of multiplications and comultiplications. This is done by expressing these structures and resolved versions of them in terms of dga maps. This same homotopy theory of dga maps applies to extract invariants beyond homological periods from systems of moduli spaces that determine systems of chains that satisfy master equations like dX + X*X = 0. Minimal models of...

Honest submodules

Pascual Jara (2007)

Czechoslovak Mathematical Journal

Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular...

Hopf-Galois extensions for monoidal Hom-Hopf algebras

Yuanyuan Chen, Liangyun Zhang (2016)

Colloquium Mathematicae

Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf algebras is shown in terms of total integrals and Hopf-Galois extensions. In addition, we obtain an affineness criterion for relative Hom-Hopf modules which is associated with faithfully flat Hopf-Galois extensions of monoidal Hom-Hopf algebras.

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