Format:
1 Online-Ressource (vi, 193 pages)
,
digital, PDF file(s).
ISBN:
9780511542855
Series Statement:
Cambridge tracts in mathematics 167
Content:
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.
Content:
Introduction -- Part I. Poincare 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
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521850643
Additional Edition:
ISBN 9780521850643
Additional Edition:
Erscheint auch als Meyer, Dagmar M. Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations Cambridge [u.a.] : Cambridge Univ. Press, 2005 ISBN 0521850649
Additional Edition:
ISBN 9780521850643
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521850643
Language:
English
Subjects:
Mathematics
Keywords:
Algebra
;
Poincaré-Dualität
;
Polynomalgebra
DOI:
10.1017/CBO9780511542855
