Level algebras with bad properties
2007 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 135, no 9, 2713-2722 p.Article in journal (Refereed) Published
This paper can be seen as a continuation of the works contained in the recent article (J. Alg., 305 (2006), 949-956) of the second author, and those of Juan Migliore (math. AC/0508067). Our results are: 1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property ( WLP). In fact, for e >> 0, we will construct a codimension three, type two h- vector of socle degree e such that all the level algebras with that h-vector do not have the WLP. We will also describe the family of those algebras and compute its dimension, for each e >> 0. 2). There exist reduced level sets of points in P-3 of type two whose artinian reductions all fail to have theWLP. Indeed, the examples constructed here have the same h- vectors we mentioned in 1). 3). For any integer r >= 3, there exist non- unimodal monomial artinian level algebras of codimension r. As an immediate consequence of this result, we obtain another proof of the fact (first shown by Migliore in the abovementioned preprint, Theorem 4.3) that, for any r >= 3, there exist reduced level sets of points in P-r whose artinian reductions are non- unimodal.
Place, publisher, year, edition, pages
2007. Vol. 135, no 9, 2713-2722 p.
type 2 level algebra, Weak Lefschetz Property, monomial algebra, non-unimodality, gorenstein artin-algebras, hilbert-functions, weak
IdentifiersURN: urn:nbn:se:kth:diva-16661ISI: 000246803000007ScopusID: 2-s2.0-42549111065OAI: oai:DiVA.org:kth-16661DiVA: diva2:334704
QC 201005252010-08-052010-08-05Bibliographically approved