Graded generalized geometry
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00360376" target="_blank" >RIV/68407700:21340/22:00360376 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.geomphys.2022.104683" target="_blank" >https://doi.org/10.1016/j.geomphys.2022.104683</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2022.104683" target="_blank" >10.1016/j.geomphys.2022.104683</a>
Alternative languages
Result language
angličtina
Original language name
Graded generalized geometry
Original language description
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular, several integrability conditions can be formulated in terms of a canonical Dorfman bracket, an example of Courant algebroid. On the other hand, smooth manifolds can be generalized to involve functions of Z-graded variables which do not necessarily commute. This leads to a mathematical theory of graded manifolds. It is only natural to combine the two theories by exploring the structures on a generalized tangent bundle associated to a given graded manifold. After recalling elementary graded geometry, graded Courant algebroids on graded vector bundles are introduced. We show that there is a canonical bracket on a generalized tangent bundle associated to a graded manifold. Graded analogues of Dirac structures and generalized complex structures are explored. We introduce differential graded Courant algebroids which can be viewed as a generalization of Q-manifolds. A definition and examples of graded Lie bialgebroids are given.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Geometry and Physics
ISSN
0393-0440
e-ISSN
1879-1662
Volume of the periodical
182
Issue of the periodical within the volume
December
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
37
Pages from-to
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UT code for WoS article
000875628400001
EID of the result in the Scopus database
2-s2.0-85139725122