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

$142.00 (C)

Part of Cambridge Tracts in Mathematics

Authors:
Dagmar M. Meyer, Georg-August-Universität, Göttingen, Germany
Larry Smith, Georg-August-Universität, Göttingen, Germany

Date Published: September 2005
availability: Available
format: Hardback
isbn: 9780521850643

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Description

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.
- 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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Reviews & endorsements
'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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Product details
- Date Published: September 2005
- format: Hardback
- isbn: 9780521850643
- length: 202 pages
- dimensions: 236 x 160 x 21 mm
- weight: 0.457kg
- contains: 5 b/w illus. 5 tables
- availability: Available
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.
Look Inside
Authors
Dagmar M. Meyer, Georg-August-Universität, Göttingen, Germany
Dagmar Meyer is Assistant Professor of Mathematics at Mathematiches Institut der Georg-August-Universität.
Larry Smith, Georg-August-Universität, Göttingen, Germany
Larry Smith is a Professor of Mathematics at Mathematiches Institut der Georg-August-Universität.