Lie Algebroids Associated with Deformed Schouten Bracket of 2-Vector Fields

2007 ◽  
pp. 147-160
Author(s):  
Kentaro Mikami ◽  
Tadayoshi Mizutani
Keyword(s):  
Vector Fields ◽  
Lie Algebroids ◽  
Schouten Bracket

Lie algebroids and homological vector fields

1997 ◽  
Vol 52 (2) ◽  
pp. 428-429 ◽  
Author(s):  
A Yu Vaintrob
Keyword(s):  
Vector Fields ◽  
Lie Algebroids

scholarly journals Variational Lie algebroids and homological evolutionary vector fields

2011 ◽  
Vol 167 (3) ◽  
pp. 772-784 ◽  
Author(s):  
A. V. Kiselev ◽  
J. W. van de Leur
Keyword(s):  
Vector Fields ◽  
Lie Algebroids

INTEGRABILITY OF PLANE FIELDS DEFINED BY 2-VECTOR FIELDS

2005 ◽  
Vol 16 (02) ◽  
pp. 197-212 ◽  
Author(s):  
KENTARO MIKAMI ◽  
TADAYOSHI MIZUTANI
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Complete Integrability ◽  
Lie Algebroids ◽  
Lie Algebroid

Given a 2-vector field on a manifold, first we briefly discuss the complete integrability of the distribution which is the image of the 2-vector field. Then we show that a new Lie algebroid is defined on such a maniold which is coincident with the cotangent Lie algebroid when the 2-vector field is Poisson. The result is extended to the case of Lie algebroids.

L∞-actions of Lie algebroids

2021 ◽  
pp. 2150013
Author(s):  
Olivier Brahic ◽  
Marco Zambon
Keyword(s):  
Vector Field ◽  
Direct Product ◽  
Vector Fields ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Geometric Structures ◽  
Courant Algebroids ◽  
Graded Manifold

We consider homotopy actions of a Lie algebroid on a graded manifold, defined as suitable [Formula: see text]-algebra morphisms. On the “semi-direct product” we construct a homological vector field that projects to the Lie algebroid. Our main theorem states that this construction is a bijection. Since several classical geometric structures can be described by homological vector fields as above, we can display many explicit examples, involving Lie algebroids (including extensions, representations up to homotopy and their cocycles) as well as transitive Courant algebroids.

scholarly journals Infinitesimal Automorphisms of VB-Groupoids and Algebroids

2019 ◽  
Vol 70 (3) ◽  
pp. 1039-1089 ◽  
Author(s):  
Chiara Esposito ◽  
Luca Vitagliano ◽  
Alfonso Giuseppe Tortorella
Keyword(s):  
Vector Bundle ◽  
Special Class ◽  
Vector Fields ◽  
Vector Bundles ◽  
Lie Algebroids ◽  
Lie Groupoids ◽  
Singular Spaces ◽  
Infinitesimal Automorphisms

Abstract VB-groupoids and algebroids are vector bundle objects in the categories of Lie groupoids and Lie algebroids, respectively, and they are related via the Lie functor. VB-groupoids and algebroids play a prominent role in Poisson and related geometries. Additionally, they can be seen as models for vector bundles over singular spaces. In this paper we study their infinitesimal automorphisms, i.e. vector fields on them generating a flow by diffeomorphisms preserving both the linear and the groupoid/algebroid structures. For a special class of VB-groupoids/algebroids coming from representations of Lie groupoids/algebroids, we prove that infinitesimal automorphisms are the same as multiplicative sections of a certain derivation VB-groupoid/algebroid.

Normal Forms and Bifurcation of Planar Vector Fields

1994 ◽  
Author(s):  
Shui-Nee Chow ◽  
Chengzhi Li ◽  
Duo Wang
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Planar Vector Fields ◽  
Planar Vector

Parallel Computation of Complex Antennas around the Coated Object Using Iterative Vector Fields Technique

2014 ◽  
Vol E97.C (7) ◽  
pp. 661-669
Author(s):  
Ying YAN ◽  
Xunwang ZHAO ◽  
Yu ZHANG ◽  
Changhong LIANG ◽  
Zhewang MA
Keyword(s):  
Parallel Computation ◽  
Vector Fields

Differential p-forms and q-vector fields with constant coefficients

2020 ◽  
pp. 1
Author(s):  
Jaime Muñoz Masqué ◽  
Luis M. Pozo Coronado ◽  
M. Eugenia Rosado
Keyword(s):  
Vector Fields ◽  
Constant Coefficients ◽  
Q Vector
Sign in / Sign up

Export Citation Format

Share Document