SEMIHOLONOMIC JETS AND INDUCED MODULES IN CARTAN GEOMETRY CALCULUS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139747" target="_blank" >RIV/00216224:14310/24:00139747 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.5817/AM2024-4-191" target="_blank" >http://dx.doi.org/10.5817/AM2024-4-191</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5817/AM2024-4-191" target="_blank" >10.5817/AM2024-4-191</a>

Jazyk výsledku

angličtina

Název v původním jazyce

SEMIHOLONOMIC JETS AND INDUCED MODULES IN CARTAN GEOMETRY CALCULUS

Popis výsledku v původním jazyce

The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of all objects and tools. This idea was broadened essentially by Elie Cartan in the beginning of the last century, and we may consider (curved) geometries as modelled over certain (flat) Klein's models. The aim of this short survey is to explain carefully the basic concepts and algebraic tools built over several recent decades. We focus on the direct link between the jets of sections of homogeneous bundles and the associated induced modules, allowing us to understand the overall structure of invariant linear differential operators in purely algebraic terms. This allows us to extend essential parts of the concepts and procedures to the curved cases.

Název v anglickém jazyce

SEMIHOLONOMIC JETS AND INDUCED MODULES IN CARTAN GEOMETRY CALCULUS

Popis výsledku anglicky

The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of all objects and tools. This idea was broadened essentially by Elie Cartan in the beginning of the last century, and we may consider (curved) geometries as modelled over certain (flat) Klein's models. The aim of this short survey is to explain carefully the basic concepts and algebraic tools built over several recent decades. We focus on the direct link between the jets of sections of homogeneous bundles and the associated induced modules, allowing us to understand the overall structure of invariant linear differential operators in purely algebraic terms. This allows us to extend essential parts of the concepts and procedures to the curved cases.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Archivum Mathematicum

ISSN

1212-5059

e-ISSN

—

Svazek periodika

60

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

29

Strana od-do

191-219

Kód UT WoS článku

001415319100001

EID výsledku v databázi Scopus

2-s2.0-85211349615