Related papers: Unimodular L-infinity algebras

Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the…

We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative $K$-algebra $R$ and we prove that it is homotopy abelian over $K$, while it is generally not formal over…

The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…

For any L-infinity algebra L, we construct an A-infinity structure on the space of symmetric tensors Sym*(L), which generalizes the classical universal enveloping for Lie algebras. Our construction is based on an invariant homotopy on a…

We find for each simple finitary Lie algebra $\mathfrak{g}$ a category $\mathbb{T}_\mathfrak{g}$ of integrable modules in which the tensor product of copies of the natural and conatural modules are injective. The objects in…

Using a homotopy introduced by de Wilde and Lecomte and homological perturbation theory for $A_\infty$-algebras, we give an explicit proof that the universal enveloping algebra $UL$ of a differential graded Lie algebra $L$ is Koszul, via an…

We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as…

We consider versal deformations of 0|3-dimensional L-infinity algebras, which correspond precisely to ordinary (non-graded) three dimensional Lie algebras. The classification of such algebras over C is well known, although we shall give a…

Explicit constructions for the minimal models of general and unimodular L-infinity algebra structures are given using the BV-formalism of mathematical physics and the perturbative expansions of integrals. In particular, the general formulas…

Let $L$ be a finite dimensional Lie algebra over a field of characteristic $0$. Then by the original Levi theorem, $L = B \oplus R$ where $R$ is the solvable radical and $B$ is some maximal semisimple subalgebra. We prove that if $L$ is an…

This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…

We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on…

This article explores some simple examples of L-infinity algebras and the construction of miniversal deformations of these structures. Among other things, it is shown that there are two families of nonequivalent L-infinity structures on a…

We apply the effective integration theory of Lie-graph algebras, developed recently by the authors, to the deformation and homotopy theories of types of bialgebras, that is structures controlled by a properad, like associative bialgebras,…