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

A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.

Dagmar M. Meyer (Author), Larry Smith (Author)

9780521850643, Cambridge University Press

Hardback, published 18 August 2005

202 pages, 5 b/w illus. 5 tables
23.6 x 16 x 2.1 cm, 0.457 kg

'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

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.

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.

Subject Areas: Algebra [PBF]