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Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations // Dagmar M. Meyer and Larry Smith.
其他題名:	Poincaré Duality Algebras, Macaulay's Dual Systems, & Steenrod Operations
作者:	Meyer, Dagmar M.,
其他作者:	Smith, L.
面頁冊數:	1 online resource (vi, 193 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Steenrod algebra. -
電子資源:	https://doi.org/10.1017/CBO9780511542855
ISBN:	9780511542855 (ebook)

Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations /
Meyer, Dagmar M.,

Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations /Poincaré Duality Algebras, Macaulay's Dual Systems, & Steenrod OperationsDagmar M. Meyer and Larry Smith. - 1 online resource (vi, 193 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;167. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9780511542855 (ebook)Subjects--Topical Terms:

908449
Steenrod algebra.

LC Class. No.: QA612.782 / .M49 2005

Dewey Class. No.: 514.2

Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations /
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505 0 $a 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.
520 $a 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.
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