scholarly journals Local and global integrability of Lie brackets

2021 ◽  
Vol 13 (3) ◽  
pp. 355
Author(s):  
Rui L. Fernandes ◽  
Yuxuan Zhang
Keyword(s):  
Lie Algebroid ◽  
Geometric Structures ◽  
Global Integrability ◽  
Lie Brackets

<p style='text-indent:20px;'>We survey recent results on the local and global integrability of a Lie algebroid, as well as the integrability of infinitesimal multiplicative geometric structures on it.</p>

scholarly journals On local integration of Lie brackets

2020 ◽  
Vol 2020 (760) ◽  
pp. 267-293 ◽  
Author(s):  
Alejandro Cabrera ◽  
Ioan Mărcuţ ◽  
María Amelia Salazar
Keyword(s):  
Vector Field ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Lie Theory ◽  
Lie Groupoids ◽  
Lie Groupoid ◽  
Finite Dimensional ◽  
Local Integration ◽  
Lie Brackets ◽  
Complete Account

AbstractWe give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional proof of the fact that the category of germs of local Lie groupoids is equivalent to that 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.

Highly Efficient Solar-driven Photocatalytic Hydrogen Evolution by Ternary 3D ZnIn2S4-MoS2 Microsphere/1D TiO2 Nanobelt Heterostructure

2021 ◽  
Author(s):  
Hanghang Zhou ◽  
Lan Wang ◽  
Hang Shi ◽  
Huan Zhang ◽  
Yue Wang ◽  
...  
Keyword(s):  
Energy Level ◽  
High Activity ◽  
Hydrogen Evolution ◽  
Solvothermal Method ◽  
Semiconductor Materials ◽  
Effective Strategy ◽  
Geometric Structures ◽  
Photocatalytic Hydrogen Evolution ◽  
Highly Efficient ◽  
Tio2 Nanobelts

Combining different semiconductor materials with diverse geometric structures and energy level configurations is an effective strategy for constructing high-activity heterostructure photocatalyst. Using the solvothermal method, 1D TiO2 nanobelts were uniformly...

scholarly journals The geometric structures and instability of entropic dynamical models

2011 ◽  
Vol 227 (1) ◽  
pp. 459-471 ◽  
Author(s):  
Linyu Peng ◽  
Huafei Sun ◽  
Dandi Sun ◽  
Jin Yi
Keyword(s):  
Dynamical Models ◽  
Geometric Structures
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