Bounded reduction for Chevalley groups of types $E_6$ and $E_7$

Pavel Gvozdevsky

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arXiv · 2305.17012

Bounded reduction for Chevalley groups of types $E_6$ and $E_7$

Pavel Gvozdevsky

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Abstract

We prove that an element from the Chevalley group of type $E_6$ or $E_7$ over a polynomial ring with coefficients in a small-dimensional ring can be reduced to an element of certain proper subsystem subgroup by a bounded number of elementary root elements. The bound is given explicitly. This result is an effective version of the early stabilisation of the corresponding $K_1$-functor. We also give part of the proof of similar hypothesis for $E_8$.

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Pavel Gvozdevsky. 2023-05-26. Bounded reduction for Chevalley groups of types $E_6$ and $E_7$. https://arxiv.org/abs/2305.17012

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