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

by Dagmar M. Meyer, Larry Smith

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:	08/18/2005
Series:	Cambridge Tracts in Mathematics , #167
Pages:	202
Product dimensions:	6.30(w) x 9.29(h) x 0.83(d)

About the Author

Dagmar Meyer is Assistant Professor of Mathematics at Mathematiches Institut der Georg-August-Universität.

Larry Smith is a Professor of Mathematics at Mathematiches Institut der Georg-August-Universität.

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.

Editorial Reviews

'Besides the wealth of interesting results the greatest strength of the book is the many examples included which illustrate how the abstract structural results yeild effective computational tools.' Zentralblatt MATH

From the Publisher