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

Fröberg, R.; Löfwal, C.

Displaying similar documents to “Koszul homology and Lie algebras with application to generic forms and points.”

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

Avramov, Luchezar L. (2002)

Homology, Homotopy and Applications

Similarity:

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

Avramov, Luchezar L. (2002)

Homology, Homotopy and Applications

Similarity:

Homotopy Lie algebras and fundamental groups via deformation theory

Martin Markl, Stefan Papadima (1992)

Annales de l'institut Fourier

Similarity:

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.

On the homology of free Lie algebras

Calin Popescu (1998)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Given a principal ideal domain $R$ of characteristic zero, containing $1 / 2$ , and a connected differential non-negatively graded free finite type $R$ -module $V$ , we prove that the natural arrow $𝕃 F H (V) \to F H 𝕃 (V)$ is an isomorphism of graded Lie algebras over $R$ , and deduce thereby that the natural arrow $U F H 𝕃 (V) \to F H U 𝕃 (V)$ is an isomorphism of graded cocommutative Hopf algebras over $R$ ; as usual, $F$ stands for free part, $H$ for homology, $𝕃$ for free Lie algebra, and $U$ for universal enveloping algebra. Related facts and examples are also...

$C_{\infty}$ -structure on the Cohomology of the Free 2-Nilpotent Lie Algebra

Michel Dubois-Violette, Todor Popov (2013)

Publications de l'Institut Mathématique

Similarity:

On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy

Martin Markl (1989)

Annales de l'institut Fourier

Similarity:

The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type $F$ is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.

A homological characterization of graded complete intersections, II

Tadeusz Józefiak (1976)

Fundamenta Mathematicae

Similarity:

The Hochschild cohomology of a closed manifold

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

Publications Mathématiques de l'IHÉS

Similarity:

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...