Graded generalized geometry

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Graded generalized geometry

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Graded generalized geometry

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Geometry and Physics

ISSN

0393-0440

e-ISSN

1879-1662

Svazek periodika

182

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

37

Strana od-do

—

Kód UT WoS článku

000875628400001

EID výsledku v databázi Scopus

2-s2.0-85139725122