Lie algebroids, gauge theories, and compatible geometrical structures
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50015566" target="_blank" >RIV/62690094:18470/19:50015566 - isvavai.cz</a>
Result on the web
<a href="https://www.worldscientific.com/doi/abs/10.1142/S0129055X19500156" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/S0129055X19500156</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0129055X19500156" target="_blank" >10.1142/S0129055X19500156</a>
Alternative languages
Result language
angličtina
Original language name
Lie algebroids, gauge theories, and compatible geometrical structures
Original language description
The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular compatibility conditions. This paper is supposed to analyze these compatibilities from a mathematical perspective. In particular, we show that the compatibility of a connection with a Lie algebroid that one finds is the Cartan condition, introduced previously by A. Blaom. For the metric on the base M of a Lie algebroid equipped with any connection, we show that the compatibility suggested from gauge theories implies that the foliation induced by the Lie algebroid becomes a Riemannian foliation. Building upon a result of del Hoyo and Fernandes, we prove, furthermore, that every Lie algebroid integrating to a proper Lie groupoid admits a compatible Riemannian base. We also consider the case where the base is equipped with a compatible symplectic or generalized Riemannian structure.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Reviews in mathematical physics
ISSN
0129-055X
e-ISSN
—
Volume of the periodical
31
Issue of the periodical within the volume
4
Country of publishing house
SG - SINGAPORE
Number of pages
27
Pages from-to
"Article number: 1950015"
UT code for WoS article
000465086000004
EID of the result in the Scopus database
2-s2.0-85058235718