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Universally Koszul and initially Koszul properties of Orlik–Solomon algebras.
- Source :
-
Journal of Algebra & Its Applications . Nov2020, Vol. 19 Issue 11, pN.PAG-N.PAG. 21p. - Publication Year :
- 2020
-
Abstract
- Let K be a field with char (K) = 0 and E = K 〈 e 1 , ... , e n 〉 an exterior algebra over K with a standard grading deg e i = 1. Let R = E / J be a graded algebra, where J is a graded ideal in E. In this paper, we study universally Koszul and initially Koszul properties of R and find classes of ideals J which characterize such properties of R. As applications, we classify arrangements whose Orlik–Solomon algebras are universally Koszul or initially Koszul. These results are related to a long-standing question of Shelton–Yuzvinsky [B. Shelton and S. Yuzvinsky, Koszul algebras from graphs and hyperplane arrangements, J. London Math. Soc.56 (1997) 477–490]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *KOSZUL algebras
*ALGEBRA
*GROBNER bases
*HYPERPLANES
*IDEALS (Algebra)
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 19
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 145336413
- Full Text :
- https://doi.org/10.1142/S0219498820502187