Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50015565" target="_blank" >RIV/62690094:18470/19:50015565 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0393044018305734?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0393044018305734?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.geomphys.2018.09.004" target="_blank" >10.1016/j.geomphys.2018.09.004</a>

Result language

angličtina

Original language name

Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries

Original language description

Consider an anchored bundle (E, rho), i.e. a vector bundle E -&gt; M equipped with a bundle map rho: E -&gt; TM covering the identity. M. Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle to an infinite rank universal free Lie algebroid FR(E) superset of E. We adapt his construction to the case of an anchored bundle equipped with an arbitrary connection, (E, del), and show that it gives rise to a unique connection, (del) over tilde on FR(E) which is compatible with its Lie algebroid structure, thus turning (FR(E), (del) over tilde) into a Cartan-Lie algebroid. Moreover, this construction is universal: any connection-preserving vector bundle morphism from (E, del) to a Cartan-Lie Algebroid (A, (del) over bar) factors through a unique Cartan-Lie algebroid morphism from (FR(E), (del) over tilde) to (A, (del) over bar). Suppose that, in addition, M is equipped with a geometrical structure defined by some tensor field t which is compatible with (E, rho, del) in the sense of being annihilated by a natural E-connection that one can associate to these data. For example, for a Riemannian base (M, g) of an involutive anchored bundle (E, rho), this condition implies that M carries a Riemannian foliation. It is shown that every E-compatible tensor field t becomes invariant with respect to the Lie algebroid representation associated canonically to the Cartan-Lie algebroid (FR(E), (del) over tilde).

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of geometry and physics

ISSN

0393-0440

e-ISSN

—

Volume of the periodical

135

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

6

Pages from-to

1-6

UT code for WoS article

000453339800001

EID of the result in the Scopus database

2-s2.0-85054093958