Poincare Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations

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September 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. Steenrod operations also originated in algebraic topology and they provide a noncommutative tool to study commutative algebras over a Galois field. 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. Poincare Duality Quotients: Part II. Macaulay's Dual Systems and Frobenius Powers: Part III. Poincare 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.


Dagmar Meyer is Assistant Professor of Mathematics at Mathematiches Institut der Georg-August-Universitat. Larry Smith is a Professor of Mathematics at Mathematiches Institut der Georg-August-Universitat.


'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
EAN: 9780521850643
ISBN: 0521850649
Untertitel: 'Cambridge Tracts in Mathematic'. Sprache: Englisch.
Erscheinungsdatum: September 2005
Seitenanzahl: 193 Seiten
Format: gebunden
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