Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations
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Bibliographic Information
Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations
（Cambridge tracts in mathematics, 167）
Cambridge University Press, 2005
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Includes bibliographical references and index
Description and Table of Contents
Description
Poincare 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.
Table of Contents
- Introduction
- Part I. Poincare Duality Quotients: Part II. Macaulay's Dual Systems and Frobenius Powers: Part III. Poincare 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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