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

Erscheinungsjahr 2005
ISBN: 978-0-521-85064-3
Verlag: Cambridge University Press

Buch, Englisch, Band 167, 202 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 451 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Meyer, Dagmar. M

Smith, Larry

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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.

Über Autor(innen)

Meyer, Dagmar. M
Dagmar Meyer is Assistant Professor of Mathematics at Mathematiches Institut der Georg-August-Universität.

Smith, Larry
Larry Smith is a Professor of Mathematics at Mathematiches Institut der Georg-August-Universität.