Related papers: The Free Courant Algebroid
We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…
We study a new kind of Courant algebroid on Poisson manifolds, which is a variant of the generalized tangent bundle in the sense that the roles of tangent and the cotangent bundle are exchanged. Its symmetry is a semidirect product of…
We study a structure of the group of unitriangular automorphisms of a free associative algebra and a polynomial algebra and prove that this group is a semi direct product of abelian groups. Using this decomposition we describe a structure…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the…
It is shown via the principle of path independence that the (time gauge) constraint algebra derived in (Class. Quantum Grav. 5 (1988) pg. 1405) for vielbein General Relativity is a generic feature of any covariant theory formulated in a…
In this article, we study freeness of hyperplane arrangements. One of the most investigated arrangement is a graphic arrangement. Stanley proved that a graphic arrangement is free if and only if the corresponding graph is chordal and Dirac…
We study free dg-Lie algebroids over arbitrary derived schemes, and compute their universal enveloping and jet algebras. We also introduce derived twisted connections, and relate them with lifts on twisted square zero extensions. This…
In this paper we show how connections and their generalizations on transitive Lie algebroids are related to the notion of connections in the framework of the derivation-based noncommutative geometry. In order to compare the two…
We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop…
In this paper, first we introduce the notion of a $\VB$-Lie $2$-algebroid, which can be viewed as the categorification of a $\VB$-Lie algebroid. The tangent prolongation of a Lie $2$-algebroid is a $\VB$-Lie $2$-algebroid naturally. We show…
We give a ``coordinate free'' construction and prove the uniqueness of the vertex algebroid which gives rise to the chiral de Rham complex.
The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate…
In this paper, we study compatible Leibniz algebras. We characterize compatible Leibniz algebras in terms of Maurer-Cartan elements of a suitable differential graded Lie algebra. We define a cohomology theory of compatible Leibniz algebras…
I. M. Gelfand and D. B. Fuks have studied the cohomology of the Lie algebra of vector fields on a manifold. In this article, we generalize their main tools to compute the Leibniz cohomology, by extending the two spectral sequences…
We classify all the Heisenberg and conformal vectors and determine the full automorphism group of the free bosonic vertex algebra without gradation. To describe it we introduce a notion of inner automorphisms of a vertex algebra.
Motivated from target space covariant formulations of topological sigma models and from a graded-geometric approach to higher gauge theory, we study connections on Lie and Courant algebroids and on their description as differential graded…
In this paper, we give the notion of a CLWX 2-algebroid and show that a QP-structure of degree 3 gives rise to a CLWX 2-algebroid. This is the higher analogue of the result that a QP-structure of degree 2 gives rise to a Courant algebroid.…
By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on nongraded symplectic plane. It will be proved that the…
We propose a new class of sigma models based on Courant sigma models. We refer to these models as gauged Courant sigma models (GCSMs). By introducing additional gauge symmetries, such as those associated with a Lie group, a Lie groupoid (or…