A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Constructing -Lie algebroids via connections
New generalized Lie algebroids solve optimal control problems.
Almost Lie algebroids extend Lie algebroids with a Jacobiator, leading to characteristic classes.
Defines Dirac pairs on Jacobi algebroids, generalizing Lie algebroids.
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (…
Generalizes Kodaira vanishing theorem to Kahler Lie algebroids.
Homotopy invariance proven for twisted Lie algebroid cohomologies.
Simplified definition of LA-Courant algebroids and Poisson Lie 2-algebroids.
Paper introduces Lie algebroid index theory and a generalized Riemann-Roch theorem.
Study examines Lie algebroids with homological sections, generalizing Q-manifolds and Lie superalgebras.
We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated Courant algebroid is obtained. We introduce the notion of a morphism of quasi-Lie…
Defines a higher version of omni-Lie algebroid for new geometries.
We show how to reduce, under certain regularities conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with nondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosi for the reduction of Poisson-Nijenhuis manifolds. The choice of the more general framework of Lie a…
A class of metrizable vector bundles in the general framework of generalized Lie algebroids have been presented in the eight reference. Using a generalized Lie algebroid we obtain the Lie algebroid generalized tangent bundle of a vector bundle. This Lie algebroid is a new example of metrizable vector bundle. A new clas…
Study cohomology of Lie algebroids over algebraic spaces using derived functors and Čech cohomology.
Study first-order locally convex Lie algebroids in Bastiani calculus.
We define Lie and Courant algebroids on Fréchet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fréchet manifold and show that it inherits a Fréchet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\bb$-cotangent bundle Lie algebroid of a weakly sympl…
We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms associated to Lie algebroid extensions. We also define generalized morphisms, includin…
This work explores higher-order algebroids via vector bundle comorphisms.
An exterior differential calculus in the general framework of generalized Lie algebroids is presented. A theorem of Maurer-Cartan type is obtained. All results with details proofs are presented and a new point of view over exterior differential calculus for Lie algebroids is obtained. Using the theory of linear connect…
Generalizes sigma model with Lie algebroid structure and geometric conditions.
Study families of Lie algebroids on complex spaces, introducing unfoldings.
A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the categ…
Study Hamiltonian semisprays on Lie algebroids, extending Vaisman's work.
The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that any vector subbundle…
New Poisson structures defined from Lie algebroids, with conditions for existence.
The paper categorifies Lie and Courant algebroids, establishing correspondences and new constructions.
Study Hom-Lie algebroid connections on complex manifolds.
In this paper, we introduce the notion of a pre-symplectic algebroid, and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebroids. This result is the geometric generalization of the relation between left-symmetric algebras and symplectic (Frobenius) Lie algebras. A…
Introduces comomentum sections and proves they are Poisson maps.
The paper defines Hamiltonian Lie algebroids and explores their properties.
In this paper, first we modify the definition of a Hom-Lie algebroid introduced by Laurent-Gengoux and Teles and give its equivalent dual description. Many results that parallel to Lie algebroids are given. In particular, we give the notion of a Hom-Poisson manifold and show that there is a Hom-Lie algebroid structure …
Paper develops a unified framework for Lie algebroid connections on various bundles.
Generalizes Hamiltonian structures to Dirac structures for new mechanics models.
In this paper, we introduce the notion of -Courant algebroids, where is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by -Courant algebroids and provid…
We show how the relation between -manifolds and Lie algebroids extends to ``higher'' or ``non-linear'' analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that arises as a replacement of operations on sections of a Lie algebroid. When the base is a point, we obtain a generalizat…
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their relation via differentiation and integration. We also show how to extend our techniqu…
In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids and construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifo…
Study flat connections on Courant algebroids using Lie groups.
We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular substructures.
The paper studies Lie n-algebroids and their representations up to homotopy.
Lie algebroids are like infinitesimal Lie groupoids.
Involution algebroids extend Lie algebroids to tangent categories.
New invariant real rank identifies constant real Lie algebroids.
Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved the integration problem of Lie algebroids. It turns out that every Weinstein groupoid has a Lie algebroid, and every Lie a…
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
Generalizes van Est map to sheaves of sections taking values in -modules.
A generalized notion of a Lie algebroid is presented. Using this, the Lie algebroid generalized tangent bundle is obtained. A new point of view over (linear) connections theory on a fiber bundle is presented. These connections are characterized by o horizontal distribution of the Lie algebroid generalized tangent bundl…