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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