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Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations: Cambridge Tracts in Mathematics, cartea 167

Autor Dagmar M. Meyer, Larry Smith
en Limba Engleză Hardback – 17 aug 2005
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.
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Specificații

ISBN-13: 9780521850643
ISBN-10: 0521850649
Pagini: 202
Ilustrații: 5 b/w illus. 5 tables
Dimensiuni: 160 x 236 x 21 mm
Greutate: 0.43 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'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

Notă biografică


Descriere

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