The Koszul dual of the ring of three commuting matrices
DOI:
https://doi.org/10.7146/math.scand.a-14304Abstract
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.Downloads
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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