Lie algebroids, gauge theories, and compatible geometrical structures

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Lie algebroids, gauge theories, and compatible geometrical structures

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Lie algebroids, gauge theories, and compatible geometrical structures

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Reviews in mathematical physics

ISSN

0129-055X

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

27

Strana od-do

"Article number: 1950015"

Kód UT WoS článku

000465086000004

EID výsledku v databázi Scopus

2-s2.0-85058235718