Descripción
**Fecha de inicio**: 27/05/2013. **Fecha de fin**: 07/06/2013. **Hora de inicio:** 11:00. **Hora de fin:** 13:00.
The Weyl algebra is sometimes called the fundamental algebra of quantum mechanics because of its intrinsic relation to the Heisenberg uncertainty principle. We study the algebraic structure of this algebra by discovering properties which then become the topic of a separate chapter . Chapters include the following: Free algebras and algebras given by generators and relations, Noetherian and Artinian rings and modules, semisimple rings and the Goldie theorem, Lie algebra theory ,graded rings and modules,filtered rings and modules,regular rings and Auslander regular rings,the Gelfand-Kirillov dimension,projective dimension and global dimension,dimension of Weyl algebras,,Bernstein inequality ...
Motivation. The Weyl algebras are at the crossroads of the theory of rings of differential operators,general filtered rings,dimension theory,and applications in quantum physics.The algebraic structures are interesting in their own right in particular a rich mixture of graded and filtered ring theory combined with different dimensions.The course is a modern treatment of Ring Theory with extra motivation coming from several applications.