The work of Jan-Erik Roos on the cohomology of commutative rings.

Avramov, Luchezar L.

Displaying similar documents to “The work of Jan-Erik Roos on the cohomology of commutative rings.”

Homotopy Lie algebras and Poincaré series of algebras with monomial relations.

Avramov, Luchezar L. (2002)

Homology, Homotopy and Applications

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Hochschild cohomology and moduli spaces of strongly homotopy associative algebras.

Lazarev, A. (2003)

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Koszul homology and Lie algebras with application to generic forms and points.

Fröberg, R., Löfwal, C. (2002)

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A homological characterization of graded complete intersections, II

Tadeusz Józefiak (1976)

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Deformations of Batalin-Vilkovisky algebras

Olga Kravchenko (2000)

Banach Center Publications

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We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of an order higher than 2 (Koszul-Akman definition) leads to the structure of a strongly homotopy Lie algebra ( $L_{\infty}$ -algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture...

Homotopy Lie algebras and fundamental groups via deformation theory

Martin Markl, Stefan Papadima (1992)

Annales de l'institut Fourier

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We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as $π_{*} Ω S$ (the homotopy Lie algebra) or ${gr}^{*} π_{1} S$ (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.

Deformation Theory (Lecture Notes)

M. Doubek, Martin Markl, Petr Zima (2007)

Archivum Mathematicum

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First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation....

The Hochschild cohomology of a closed manifold

Yves Felix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2004)

Publications Mathématiques de l'IHÉS

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Let M be a closed orientable manifold of dimension and $𝒞^{*} (M)$ be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is a graded commutative and associative algebra. The augmentation map $ε : 𝒞^{*} (M) \to 𝑘$ induces a morphism of algebras $I : H H^{*} (𝒞^{*} (M); 𝒞^{*} (M)) \to H H^{*} (𝒞^{*} (M); 𝑘)$ . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of $H H^{*} (𝒞^{*} (M); 𝑘)$ , which is in general quite small. The algebra $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is expected to...