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

Dagmar M. Meyer, Larry Smith - Collection Cambridge Tracts in Mathematics

194 pages, parution le 23/08/2005

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Résumé

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 =/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.

Sommaire

Introduction
Poincaré Duality Quotients
Macaulay's Dual Systems and Frobenius Powers
Poincaré Duality and the Steenrod Algebra
Dickson, Symmetric, and Other Coinvariants
The Hit Problem mod 2
Macaulay's Inverse Systems and Applications
References
Notation
Index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Dagmar M. Meyer, Larry Smith
Collection	Cambridge Tracts in Mathematics
Parution	23/08/2005
Nb. de pages	194
Format	15,5 x 23,5
Couverture	Relié
Poids	456g
Intérieur	Noir et Blanc
EAN13	9780521850643
ISBN13	978-0-521-85064-3