Bounded reduction for Chevalley groups of types E₆ and E₇

2023/05/26 by Pavel Gvozdevsky, Gvozdevsky, Pavel
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2305.17012

Abstract

We prove that an element from the Chevalley group of type E₆ or E₇ 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 K₁-functor. We also give part of the proof of similar hypothesis for E₈.

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