NKGQHR · Non-commutative geometry of quantum homogeneous spaces
6РП — Действия „Мария Кюри“
- Период
- 2005-09-01 → 2007-08-31
- Финансиране от ЕС
- 130 875 €
- Участници
- 1
- Схема
- EIF
Линиите свързват координатора с партньорите. За проекти отпреди 2014 г. CORDIS не винаги дава точни координати. Тези точки са на ниво град или държава.
Накратко на български
Некомутативната геометрия изследва специални алгебри, като например квантовите хомогенни пространства, чрез прилагане на математически инструменти като Дираковите оператори. Това помага за разработването на физически модели и изучаването на теорията на Янг-Милс в квантова среда.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Цел на проекта
In global analysis or in algebraic geometry, a geometric space is described by an algebra of functions on this space. Non-commutative geometry extends this approach to geometry also to non-commutative algebras. In this way, A. Connes generalized in particular results from index theory and spin geometry. The aim of this project is to apply the methods of non-commutative geometry to so-called quantum homogeneous spaces. There are several definitions of this notion, but all of them cover a class of algebras that are obtained by quantizing the irreducible generalized flag manifolds (the irreducible compact Hermitian symmetric spaces) with respect to some Poisson bracket. For these, the proposer constructed a Dirac operator fitting into Connes and apos; concept o f a spectral triple (a non-commutative analogue of spin manifolds). Now, the main objective is to investigate quantum homogeneous spaces focusing on homological aspects.The goal is also to extend the aforementioned construction of Dirac operators for quantum flag manifolds to a larger class of quantum homogeneous spaces, and to study the algebraic properties of analogues of Clifford algebras that were involved in obtaining these Dirac operators. One of the motivations of non-commutative geometry is to make assertions about physical models in the non-commutative setting. A long-term objective of this project is to formulate and study Yang-Mills theory on quantum homogeneous spaces. P.M. Hajac, the researcher in charge at the host institution (IMPAN), has worked on such topics for about a decade and made some significant contributions to the subject. There are several groups at IMPAN and the University of Warsaw that work on related topics. Finally, the planned Transfer of Knowledge grant and quot; Non-commutative Geometry and Quantum Groups and quot; will bring some of the world and apos;s leading experts to Warsaw. Hence the proposer considers Warsaw a very good place for carrying out this project.
Оригинален текст от CORDIS (на английски).
Участници
- INSTYTUT MATEMATYCZNY, POLSKA AKADEMIA NAUK · WARSZAWAКоординаторНиво градПолша
Връзки
Данни: CORDIS, © Европейски съюз