The Koszul Dual of a Quotient Ring by the Jacobian Ideal of a Trilinear Form

Let S = k[x 0 ,..., x n−1 , y 0 ,..., y m−1 , z 0 ,..., z p−1 ] where k is a field of characteristic zero and n = m + p − 1. Let A = ∑ j,k x j+k y j z k and J be the Jacobian ideal of A. We denote the quotient ring S/J by R. In this article, we study its Koszul dual R ! and prove that for m, p ≥ 3 t...

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Bibliographic Details
Published inCommunications in algebra Vol. 35; no. 3; pp. 915 - 929
Main Authors Bartoszek, Pawel, Hreinsdóttir, Freyja
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 27.02.2007
Subjects
Jacobian ideal
Koszul dual
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Summary:Let S = k[x 0 ,..., x n−1 , y 0 ,..., y m−1 , z 0 ,..., z p−1 ] where k is a field of characteristic zero and n = m + p − 1. Let A = ∑ j,k x j+k y j z k and J be the Jacobian ideal of A. We denote the quotient ring S/J by R. In this article, we study its Koszul dual R ! and prove that for m, p ≥ 3 this is the enveloping algebra of a nilpotent Lie algebra of index 3.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870601115831