Universal central extensions of linear groups over rings of non-commutative Laurent polynomials, associated $K_1$-groups and $K_2$-groups

Ryusuke Sugawara

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arXiv · 2005.06253

Universal central extensions of linear groups over rings of non-commutative Laurent polynomials, associated $K_1$-groups and $K_2$-groups

Ryusuke Sugawara

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Abstract

We prove that linear groups over rings of non-commutative Laurent polynomials $D_{\tau}$ have Tits systems with the corresponding affine Weyl groups and have universal central extensions if $|Z(D)|\geq 5$ and $|Z(D)|\neq 9$. We also determine structures of $K_1$-groups and identify generators of $K_2$-groups.

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Ryusuke Sugawara. 2020-05-13. Universal central extensions of linear groups over rings of non-commutative Laurent polynomials, associated $K_1$-groups and $K_2$-groups. https://arxiv.org/abs/2005.06253

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