Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations / Dagmar M. Meyer and Larry Smith.

Format:

Book

Author/Creator:

Meyer, Dagmar M., author.

Smith, L. (Larry), 1942- author.

Series:

Cambridge tracts in mathematics ; 167.

Cambridge tracts in mathematics ; 167

Language:

English

Subjects (All):

Poincaré series.

Duality theory (Mathematics).

Steenrod algebra.

Physical Description:

1 online resource (vi, 193 pages) : digital, PDF file(s).

Other Title:

Poincaré Duality Algebras, Macaulay's Dual Systems, & Steenrod Operations

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

Poincaré duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras. These two ideas are tied together using basic commutative algebra involving Gorenstein algebras. Steenrod operations also originated in algebraic topology, but may best be viewed as a means of encoding the information often hidden behind the Frobenius map in characteristic p<>0. They provide a noncommutative tool to study commutative algebras over a Galois field. In this Tract the authors skilfully bring together these ideas and apply them to problems in invariant theory. A number of remarkable and unexpected interdisciplinary connections are revealed that will interest researchers in the areas of commutative algebra, invariant theory or algebraic topology.

Contents:

Introduction

Part I. Poincare Duality Quotients

Part II. Macaulay's Dual Systems and Frobenius Powers

Part III. Poincaré Duality and the Steenrod Algebra

Part IV. Dickson, Symmetric, and Other Coinvariants

Part V. The Hit Problem mod 2

Part VI. Macaulay's Inverse Systems and Applications.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-15366-2

1-280-41625-4

9786610416257

0-511-18210-4

0-511-13042-2

0-511-19934-1

0-511-30002-6

0-511-54285-2

0-511-12889-4

OCLC:

171137483