國立虎尾科技大學 |

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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations // Dagmar M. Meyer and Larry Smith.
remainder title:	Poincaré Duality Algebras, Macaulay's Dual Systems, & Steenrod Operations
Author:	Meyer, Dagmar M.,
other author:	Smith, L.
Description:	1 online resource (vi, 193 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Poincaré series. -
Online resource:	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:

904400
Poincaré series.

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

Dewey Class. No.: 514.2

Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations /
LDR:02331nam a2200313 i 4500 001 1122661
003 UkCbUP
005 20151005020622.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2005||||enk o ||1 0|eng|d
020 $a 9780511542855 (ebook)
020 $z 9780521850643 (hardback)
035 $a CR9780511542855
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA612.782 $b .M49 2005
082 0 4 $a 514.2 $2 22
100 1 $a Meyer, Dagmar M., $e author. $3 1439033
245 1 0 $a Poincaré duality algebras, Macaulay's dual systems, and Steenrod operations / $c Dagmar M. Meyer and Larry Smith.
246 3 $a Poincaré Duality Algebras, Macaulay's Dual Systems, & Steenrod Operations
264 1 $a Cambridge : $b Cambridge University Press, $c 2005.
300 $a 1 online resource (vi, 193 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
490 1 $a Cambridge tracts in mathematics ; $v 167
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
650 0 $a Poincaré series. $3 904400
650 0 $a Duality theory (Mathematics) $3 527743
650 0 $a Steenrod algebra. $3 908449
700 1 $a Smith, L. $q (Larry), $d 1942- $e author. $3 1439034
776 0 8 $i Print version: $z 9780521850643
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511542855