Presentation of affine Kac–Moody groups over rings

@article{Allcock2016PresentationOA,
  title={Presentation of affine Kac–Moody groups over rings},
  author={Daniel Allcock},
  journal={Algebra & Number Theory},
  year={2016},
  volume={10},
  pages={533-556}
}
  • Daniel Allcock
  • Published 2016
  • Mathematics
  • Algebra & Number Theory
  • Tits has defined Steinberg groups and Kac-Moody groups for any root system and any commutative ring R. We establish a Curtis-Tits-style presentation for the Steinberg group St of any rank > 2 irreducible affine root system, for any R. Namely, St is the direct limit of the Steinberg groups coming from the 1- and 2-node subdiagrams of the Dynkin diagram. This leads to a completely explicit presentation. Using this we show that St is finitely presented if the rank is > 3 and R is finitely… CONTINUE READING

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