Poincare Duality Algebras, Macaulay''s Dual Systems, and Steenrod Operations
Book Details
Format
Hardback or Cased Book
Book Series
Cambridge Tracts in Mathematics
ISBN-10
0521850649
ISBN-13
9780521850643
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Aug 18th, 2005
Print length
202 Pages
Weight
440 grams
Dimensions
16.00 x 23.60 x 1.80 cms
Product Classification:
Algebraic topology
Ksh 21,800.00
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As the title suggests, in this Tract the authors skilfully bring together several key notions 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.
Poincare 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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