Generalized Castelnuovo-Mumford regularity for affine Kac-Moody algebras

Seok Jin Kang, Dong Il Lee, Euiyong Park, Hyungju Park

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4 Scopus citations


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.

Original languageEnglish
Pages (from-to)13-22
Number of pages10
JournalJournal of Algebra
Issue number1
StatePublished - 1 Sep 2011


  • Affine Kac-Moody algebras
  • Castelnuovo-Mumford regularity
  • Highest weight representations


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