Abstract
Tits has defined Steinberg groups and Kac–Moody groups for any root system and any commutative ring . We establish a Curtis–Tits-style presentation for the Steinberg group of any irreducible affine root system with rank , for any . Namely, is the direct limit of the Steinberg groups coming from the - and -node subdiagrams of the Dynkin diagram. In fact, we give a completely explicit presentation. Using this we show that is finitely presented if the rank is and is finitely generated as a ring, or if the rank is and is finitely generated as a module over a subring generated by finitely many units. Similar results hold for the corresponding Kac–Moody groups when is a Dedekind domain of arithmetic type.
Citation
Daniel Allcock. "Presentation of affine Kac–Moody groups over rings." Algebra Number Theory 10 (3) 533 - 556, 2016. https://doi.org/10.2140/ant.2016.10.533
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