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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

  • 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

  • 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

  • UT code for WoS article

    000875628400001

  • EID of the result in the Scopus database

    2-s2.0-85139725122