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  3. Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations
  • Cited by 30
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2005
Online ISBN:
9780511542855
DOI:
https://doi.org/10.1017/CBO9780511542855
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
Cambridge Tracts in Mathematics (167)
Information

Book description

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.

Reviews

'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.'

Source: Zentralblatt MATH

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