Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations
Part of Cambridge Tracts in Mathematics
- Dagmar M. Meyer, Georg-August-Universität, Göttingen, Germany
- Larry Smith, Georg-August-Universität, Göttingen, Germany
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 p0. 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.Read more
- Recasts a long forgotten but powerful theory in current terminology
- Makes extensive use of illustrative examples
- Brings to light unexpected interdisciplinary applications
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'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
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- Date Published: October 2005
- format: Adobe eBook Reader
- isbn: 9780511128240
- contains: 5 b/w illus. 5 tables
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
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
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