Related papers: L-infinity Algebras From Multicontact Geometry
In "Lie infinity algebras and higher analogues of Dirac structures and Courant algebroids" [arXiv:1003.1004], Marco Zambon constructs an $L_\infty$-algebra associated with any higher standard or twisted Courant algebroid (also known as a…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer-Cartan algebra-the familiar differential graded algebra of alternating forms on g with values in the ground field, endowed with the…
The notion of Lie algebroids over a topological ringed space provides a unified framework to study various geometric structures. This geometric concept is intimately connected with well-known algebraic structures, including Gerstenhaber…
In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…
In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…
In this lecutre note, we consider infinite dimensional Lie algebras of generalized Jacobi matrices $\mathfrak{g}J(k)$ and $\mathfrak{gl}_\infty(k)$, which are important in soliton theory, and their orthogonal and symplectic subalgebras. In…
We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.
We establish a relation between higher contact-like structures on supermanifolds and the N = 1 super-Poincare group via its superspace realisation. To do this we introduce a vector-valued contact structure, which we refer to as a…
The notion of an F-manifold algebra is the underlying algebraic structure of an $F$-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding…
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…
In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.
This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations…
This document is a reorganization of the results on the Master Thesis of the same title written by the author under the supervision of Dr. Christian Blohmann at the University of Bonn in 2014. There are three main results in this document.…
On a manifold with an almost contact metric structure $(\varphi,\vec\xi,\eta,g,X,D)$ the notions of the interior and the $N$-prolonged connections are introduced. Using the $N$-prolonged connection, a new almost contact metric structure is…
In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a…
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant…
We study CR-manifolds of arbitrary CR codimension, mainly focusing on Levi and contact-nondegeneracy and depth. We investigate these and other invariants in the locally homogeneous case, developing a comprehensive theory which establishes…
Let g be a semisimple Lie algebra over an algebraically closed field K of characteristic 0 and O be a nilpotent orbit in g. Then Orb is a symplectic algebraic variety and one can ask whether it is possible to quantize $\Orb$ (in an…
A complex contact threefold is a threefold with a two-dimensional non-integrable holomorphic distribution. A contact curve on a contact threefold is an integrable curve of the distribution. This work was inspired by two papers of Bryant, in…