2016/09/07 by Weyman, Jerzy
#Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1609.02083
In this paper I give an explicit construction of the generic ring Rgen for finite free resolutions of length 3. The corresponding problem for resolutions of length 2 was solved in 1970'ies by Hochster and Huneke. The key role is played by the defect Lie algebra introduced in my old work on the subject. The defect Lie algebra turns out to be a parabolic Lie algebra in a Kac-Moody Lie algebra associated to the graph Tp,q,r corresponding to the format of the resolution. The ring Rgen is Noetherian if and only if the graph Tp.q.r is a Dynkin graph.