The Koszul dual of the ring of three commuting matrices

Authors

  • Freyja Hreinsdóttir

DOI:

https://doi.org/10.7146/math.scand.a-14304

Abstract

Let X=(xij),Y=(yij) and Z=(zij) be generic n by n matrices. Let k be a field with char k2,3,S=k[x11,,xnn,y11,,ynn,z11,,znn] and let I be the ideal generated by the entries of the matrices XYYX,XZZX and YZZY. We study the Koszul dual of the ring R=S/I and show that for n3 this is the enveloping algebra of a nilpotent Lie algebra. We also give the dimension of the Lie algebra in each degree.

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Published

2000-12-01

How to Cite

Hreinsdóttir, F. (2000). The Koszul dual of the ring of three commuting matrices. MATHEMATICA SCANDINAVICA, 87(2), 161–199. https://doi.org/10.7146/math.scand.a-14304

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Articles