Description: Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology. Dagmar M. Meyer (Author), Larry Smith (Author) 9780521850643, Cambridge University Press Hardback, published 18 August 2005 202 pages 23.6 x 16 x 2.1 cm, 0.457 kg '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 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. 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. Subject Areas: Algebra [PBF]
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BIC Subject Area 1: Algebra [PBF]
Number of Pages: 202 Pages
Publication Name: Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations
Language: English
Publisher: Cambridge University Press
Item Height: 236 mm
Subject: Mathematics
Publication Year: 2005
Type: Textbook
Item Weight: 457 g
Author: Larry Smith, Dagmar M. Meyer
Item Width: 160 mm
Series: Cambridge Tracts in Mathematics
Format: Hardcover
