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

Autor:	Gvozdevsky, Pavel
Rok vydání:	2023
Předmět:	Mathematics - Group Theory 19B14(primary) 19B10 20G35 20G41(secondary)
Druh dokumentu:	Working Paper
Popis:	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 $E_8$. Comment: 32 pages, 7 figures, submitted to "European Journal of Mathematics". arXiv admin note: substantial text overlap with arXiv:2106.12697
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.17012 Zobrazit plný text záznamu View this record from Arxiv