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## Project

# Calabi-Yau property of Hopf algebras (R-2340)

Calabi-Yau categories came from Mathematical Physics and Algebraic Geometry. The Serre functor in the bounded derived category of coherent sheaves on a Calabi-Yau variety is an iteration of the shift functor. Triangulated categories with this property are called Calabi-Yau categories. An algebra is a Calabi-Yau algebra, if the associated bounded derived category of all finite dimensional modules is a Calabi-Yau category. From this definition, a finite dimensional Calabi-Yau algebra must be semisimple. However, for a finite dimensional selfinjective algebra, its stable module category is a triangulated category. A selfinjective algebra is called a stably Calabi-Yau algebra if its stable category is Calabi-Yau. Calabi-Yau categories and (stably) Calabi-Yau algebras are now popular in many braches of mathematics, such as representation theory, algebraic geometry, mathematical physics and so on. Hopf algebras, as a special kind of algebras endowed with coalgebra structure have been extensively studied since they were introduced in 1940s. In this project we study the Calabi-Yau property of Hopf algebras. This project will deal with the following problems.

Date:1 Apr 2010
→
31 Dec 2011

Keywords:ENVELOPING ALGEBRAS OF LIE ALGEBRAS, INVARIANT THEORY, NON-COMMUTATIVE ALGEBRAIC GEOMETRY, NON-COMMUTATIVE RINGS

Disciplines:Mathematical sciences