The Koszul dual of the ring of three commuting matrices

Freyja Hreinsdóttir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let X = (xij), Y = (yij) and Z = (zij) be generic n by n matrices. Let k be a field with char k ≠ 2, 3, S = k-[x11, . . . , xnn, y11, . . . , ynn, z11, . . . , znn] and let I be the ideal generated by the entries of the matrices XY - YX, XZ - ZX and YZ - ZY. We study the Koszul dual of the ring R = S/I and show that for n ≥ 3 this is the enveloping algebra of a nilpotent Lie algebra. We also give the dimension of the Lie algebra in each degree.

Original languageEnglish
Pages (from-to)161-199
Number of pages39
JournalMathematica Scandinavica
Issue number2
Publication statusPublished - 2000


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