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Rational Representations, The Steenrod Algebra and Functor Homology

Vincent Franjou Université de Nantes, Nantes, France
Eric M. Friedlander Northwestern University, Evanston, IL
Teimuraz Pirashvili A. M. Razmadze Mathematical Institute, Tbilisi, Republic of Georgia
Lionel Schwartz Université Paris XIII, Villetaneuse, France
A publication of the Société Mathématique de France
Available Formats:
Softcover ISBN: 978-2-85629-159-7
Product Code: PASY/16
List Price: $36.00 AMS Member Price:$28.80
Please note AMS points can not be used for this product
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Rational Representations, The Steenrod Algebra and Functor Homology
Vincent Franjou Université de Nantes, Nantes, France
Eric M. Friedlander Northwestern University, Evanston, IL
Teimuraz Pirashvili A. M. Razmadze Mathematical Institute, Tbilisi, Republic of Georgia
Lionel Schwartz Université Paris XIII, Villetaneuse, France
A publication of the Société Mathématique de France
Available Formats:
 Softcover ISBN: 978-2-85629-159-7 Product Code: PASY/16
 List Price: $36.00 AMS Member Price:$28.80
Please note AMS points can not be used for this product
• Book Details

Panoramas et Synthèses
Volume: 162004; 132 pp
MSC: Primary 14; 18; 19; 55;

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.

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

• Request Review Copy
Volume: 162004; 132 pp
MSC: Primary 14; 18; 19; 55;

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.