Universally Koszul and initially Koszul properties of Orlik–Solomon algebras.

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]