Differential geometry in braided categories

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Project objective

My research project is dedicated to the study of braided non-commutative differential geometry which has one of its origins in the theory of quantum groups. I am interested in the construction of braided analogues of (bicovariant) differential calculi on (Hopf) algebras, and in the study of Hochschild and cyclic homology in braided abelian categories. I want to find out if there exist similar close relations between these braided structures as in the classical symmetric case where the objects usually are modules over a commutative ring k. Training content (objective, benefit and expected impact) The project generalizes structures of non-commutative differential geometry to braided categories. Extensive use has to be made of categorical methods in braided abelian (ribbon) categories as well as of homology and of differential geometry on (bi- and Hopf) algebras. suitable generalization of these structures to braided categories have to be found. The enlargement of my knowledge and skills through the project will help me to continue my work in the feld of braided mathematics" and to advance also in other fields of mathematics like low-dimensional topology and Topological Quantum Field Theories. "

Original text from CORDIS.

Participants

• University of Cambridge · CambridgeCoordinatorUnited Kingdom
• Not availableCity levelGermany

Links

• View on CORDIS