Modular Representation Theory of Finite Groups

"In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavors. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory is a branch of mathematics, and that part of representation theory that studies linear representations of finite groups over a field K of positive characteristic. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory. This book aims to the modular representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra."