Generalized Castelnuovo–Mumford regularity for affine Kac–Moody algebras

The graded modules over noncommutative algebras often have minimal free resolutions of infinite length, resulting in infinite Castelnuovo–Mumford regularity. In Kang et al. (2010) [6], we introduced a generalized notion of Castelnuovo–Mumford regularity to overcome this difficulty. In this paper, we compute the generalized Castelnuovo–Mumford regularity for integrable highest weight representations of all affine Kac–Moody algebras. It is shown that the generalized regularity depends only on the type and rank of algebras and the level of representations.