首页|Decompositions of matrices over division algebras into products of commutators
Decompositions of matrices over division algebras into products of commutators
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NSTL
Elsevier
Let D be a division algebra of degree m. The first aim of this paper is to show that if D is tame and totally ramifield and if the center of D is Henselian, then there exists a positive d depending on m such that every element in the commutator subgroup D? of the unit group D* = D \ {0} is a product at most d commutators, which answers a problem of P. Draxl ([5], Problem 1, Page 102) for tame and totally ramifield division algebras whose centers are Henselian. The second goal is to prove that if D is infinite and every element in D? is a product at most alpha commutators in D*, then every matrix in the special linear group SLn(D) of degree n > 1 is a product of at most 2 + 6 alpha commutators of involutions. (C) 2022 Elsevier Inc. All rights reserved.
Division algebraMatrix decompositionCommutatorCommutator widthSkew linear group
Mai Hoang Bien、Truong Huu Dung、Nguyen Thi Thai Ha、Tran Nam Son
NSTL
Elsevier
