MISC

2007年5月

The strong Lefschetz property for Artinian algebras with non-standard grading

JOURNAL OF ALGEBRA
  • Tadahito Harima
  • ,
  • Junzo Watanabe

311
2
開始ページ
511
終了ページ
537
記述言語
英語
掲載種別
DOI
10.1016/j.jalgebra.2007.01.019
出版者・発行元
ACADEMIC PRESS INC ELSEVIER SCIENCE

Let A = circle plus(c)(i=0) A(i) be a graded Artinian K-algebra, where A(c) not equal (0) and char K = 0. (The grading may not necessarily be standard.) Then A has the strong Lefschetz property if there exists an element g is an element of A(1) such that the multiplication x g(c-2i) : A(i) -> A(c-i) is bijective for every i = 0, 1, . . . , [c/2]. The main results obtained in this paper are as follows:
1. A has the strong Lefschetz property if and only if there is a linear form z is an element of A(1) such that Gr((z))(A) has the strong Lefschetz property.
2. If A is Gorenstein, then A has the strong Lefschetz property if and only if there is a linear form z is an element of A such that all central simple modules of (A, z) have the strong Lefischetz property.
3. A finite free extension of an Artinian K-algebra with the strong Lefschetz property has the strong Lefschetz property if the fiber does.
4. The complete intersection defined by power sums of consecutive degrees has the strong Lefschetz property. (c) 2007 Elsevier Inc. All rights reserved.

リンク情報
DOI
https://doi.org/10.1016/j.jalgebra.2007.01.019
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000246345300004&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.jalgebra.2007.01.019
  • ISSN : 0021-8693
  • Web of Science ID : WOS:000246345300004

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