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].