Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations

Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations

by Dagmar M. Meyer, Larry Smith
     
 

ISBN-10: 0521850649

ISBN-13: 9780521850643

Pub. Date: 08/31/2005

Publisher: Cambridge University Press

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. Steenrod operations also originated in algebraic topology and they provide a noncommutative tool to study commutative algebras over a Galois field. The authors skilfully

Overview

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. Steenrod operations also originated in algebraic topology and they provide a noncommutative tool to study commutative algebras over a Galois field. 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.

Product Details

ISBN-13:
9780521850643
Publisher:
Cambridge University Press
Publication date:
08/31/2005
Series:
Cambridge Tracts in Mathematics Series, #167
Pages:
202
Product dimensions:
5.98(w) x 8.98(h) x 0.83(d)

Table of Contents

Introduction; Part I. Poincaré 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: References; Notation; Index.

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