# Rational Representations, The Steenrod Algebra and Functor Homology

Share this page
*Vincent Franjou; Eric M. Friedlander; Teimuraz Pirashvili; Lionel Schwartz*

A publication of the Société Mathématique de France

The book presents aspects of homological algebra in functor categories, with
emphasis on polynomial functors between vector spaces over a finite field. With
these foundations in place, the book presents applications to representation
theory, algebraic topology and \(K\)-theory. As these applications reveal,
functor categories offer powerful computational techniques and theoretical
insights.

T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander
then presents applications to the rational representations of general linear
groups. L. Schwartz emphasizes the relation of functor categories to the
Steenrod algebra. Finally, V. Franjou and T. Pirashvili present
A. Scorichenko's understanding of the stable \(K\)-theory of rings as functor
homology.

The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.