JOURNAL OF ALGEBRA | 卷:551 |
The absolutely Koszul and Backelin-Roos properties for spaces of quadrics of small codimension | |
Article | |
Maleki, Rasoul Ahangari1  Sega, Liana M.2  | |
[1] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran | |
[2] Univ Missouri, Dept Math & Stat, Kansas City, MO 64110 USA | |
关键词: Koszul algebra; Golod homomorphism; DG algebra; | |
DOI : 10.1016/j.jalgebra.2020.01.019 | |
来源: Elsevier | |
【 摘 要 】
Let k be a field, R a standard graded quadratic k-algebra with dim(k) R-2 <= 3, and let (k) over bar denote an algebraic closure of k. We construct a graded surjective Golod homomorphism phi: P -> R circle times(k)-> k such that P is a complete intersection of codimension at most 3. Furthermore, we show that R is absolutely Koszul (that is, every finitely generated R-module has finite linearity defect) if and only if R is Koszul if and only if R is not a trivial fiber extension of a standard graded k-algebra with Hilbert series (1 + 2t - 2t(3))(1 - t)(-1) In particular, we recover earlier results on the Koszul property of Backelin [4], Conca [7] and D'Ali [11]. (C) 2020 Elsevier Inc. All rights reserved.
【 授权许可】
Free
【 预 览 】
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