DIFFERENTIAL GRADED LIE GROUPS AND THEIR DIFFERENTIAL GRADED LIE ALGEBRAS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019910" target="_blank" >RIV/62690094:18470/22:50019910 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00031-021-09666-9" target="_blank" >https://link.springer.com/article/10.1007/s00031-021-09666-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00031-021-09666-9" target="_blank" >10.1007/s00031-021-09666-9</a>

Result language
angličtina
Original language name
DIFFERENTIAL GRADED LIE GROUPS AND THEIR DIFFERENTIAL GRADED LIE ALGEBRAS
Original language description
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of integration in the context, and recollect the known results. Then, we define the category of differential graded Lie groups and study its properties. We show how to associate a differential graded Lie algebra to every differential graded Lie group and vice versa. For the DGLA -> DGLG direction, the main "tools" are graded Hopf algebras and Harish-Chandra pairs (HCP)-we define the category of graded and differential graded HCPs and explain how those are related to the desired construction. We describe some near-at-hand examples and mention possible generalizations.
Czech name
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Czech description
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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

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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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