Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations

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Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations / Dagmar Meyer and Larry Smith

資料種別:

図書

出版情報:

Cambridge ; New York : Cambridge University Press, 2005

形態:

vi, 193 p. ; 24 cm

シリーズ名:

Cambridge tracts in mathematics ; 167 <BA00134372>

著者名:

ISBN:

9780521850643 [0521850649]

書誌ID:

BA73033864

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Duality theory (Mathematics); Poincaré series; Steenrod algebra

言語:

英語

目次情報:

Introduction

Poincare duality quotients / Part I：

Poincare duality, Gorenstein algebras, and irreducible ideals / I.1：

Properties of irreducible ideals / I.2：

The ancestor ideals / I.3：

Fundamental classes / I.4：

Poincare duality quotients of F[V] / I.5：

Counting Poincare duality quotients up to isomorphism / I.6：

Macaulay's dual systems and Frobenius powers / Part II：

Divided power algebras and operations / II.1：

Macaulay's dual principal systems / II.2：

An illustrative example / II.3：

Relation to the classical form problem / II.4：

The K [subset or is implied by] L Paradigm: a computational tool / II.5：

Frobenius powers / II.6：

Poincare duality and the Steenrod algebra / Part III：

P*-Unstable Poincare duality quotients of F[subscript q] [V] / III.1：

The P*-Double Annihilator Theorem / III.2：

Wu classes / III.3：

P*-Indecomposables: Hit Problems / III.4：

A dual interpretation of the P*-Double Annihilator Theorem / III.5：

Steenrod operations and Frobenius powers / III.6：

Examples / III.7：

Dickson, symmetric, and other coinvariants / Part IV：

Dickson coinvariants / IV.1：

Wu classes of algebras of coinvariants / IV.2：

The Macaulay dual of Dickson coinvariants mod 2 / IV.3：

Symmetric coinvariants / IV.4：

The Hit Problem mod 2 / Part V：

Powers of Dickson polynomials in 2 variables / V.1：

A*-Indecomposable elements in F[subscript 2] [x, y] / V.2：

Powers of Dickson polynomials in 3 variables / V.3：

Powers of Dickson polynomials in many variables / V.4：

Powers of mod 2 Stiefel-Whitney classes in 3 variables / V.5：

Macaulay's inverse systems and applications / Part VI：

Macaulay's inverse principal systems / VI.1：

Catalecticant Matrices and Ancestor Ideals / VI.2：

Regular ideals / VI.3：

Lying over for irreducible ideals / VI.4：

Change of rings and inverse polynomials / VI.5：

Inverse systems and the Steenrod algebra / VI.6：

Change of Rings and Wu Classes / VI.7：

The Hit Problem for the Dickson and other algebras / VI.8：

References

Notation

Index

Introduction

Poincare duality quotients / Part I：

Poincare duality, Gorenstein algebras, and irreducible ideals / I.1：

Properties of irreducible ideals / I.2：

The ancestor ideals / I.3：

Fundamental classes / I.4：

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