主 题: Generic kernels and other constructions
报告人: Prof.Jon F. Carlson (University of Georgia)
时 间: 2009-05-28 下午16:00 - 17:00
地 点: 资源大厦1328
This is a report on joint work with Eric Friedlander, Julia Pevtsova
and Andrei Suslin. The idea is to define some canonical submodule and
properties for modules over modular group algebras. We are particularly
interested in modules over elementary abelian groups. We define the
notion of the generic kernel of a module. For an elementary abelian
group, this submodule has a very special property called the equal
images property. The dual notion is the generic image, a submodule having
the equal kernels poperty. When the module M has constant Jordan type,
and the group G is elementary abelian of rank 2, then the constructions
give a very interesting filtration with completely reducible factors
on M. In the case of an elementary abelian p-group of rank 2, there is
an interesting class of modules, which we call W modules, that play
the role of projectives in the category of modules with the equal
images property.
