Angelo Calil Bianchi
IMECC-UNICAMP, Brazil
Truncated graded modules for Lie algebras.
Abstract: This work is dedicated to the study of some homological properties of the category of graded modules for a graded Lie algebra with finite-dimensional graded components. In particular, we construct certain full subcategories of this category obtained by choosing its simple objects in a way that we are able to compute their space of extensions. We then focus on the truncated modules and compute their graded character under certain conditions. Finally, we give a presentation of these truncated modules in terms of generators and relations which allows us to regard these modules as generalizations of restricted Kirillov-Reshetikhin modules.