A note on the existence of nontrivial homomorphism e n (R) → e n-1 (R)

Hong You

doi:10.1142/S0219498817500104

A note on the existence of nontrivial homomorphism e n (R) → e _n-1 (R)

Hong You^*

^*Corresponding author for this work

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that there is no nontrivial group homomorphism En(R) → E_n-1(R) over commutative local rings and division rings for n ≥ 3, respectively. It gives a negative answer to Ye's problem (see [S. K. Ye, Low-dimensional representations of matrix group actions on CAT(0) spaces and manifolds, J. Algebra 409 (2014) 219-243]) for the above rings.

Original language	English
Article number	17500104
Journal	Journal of Algebra and its Applications
Volume	16
Issue number	1
DOIs	https://doi.org/10.1142/S0219498817500104
Publication status	Published - 1 Jan 2017

Keywords

Elementary group
division ring
homomorphism
local ring

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10.1142/S0219498817500104

Cite this

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title = "A note on the existence of nontrivial homomorphism e n (R) → e n-1 (R)",

abstract = "We show that there is no nontrivial group homomorphism En(R) → En-1(R) over commutative local rings and division rings for n ≥ 3, respectively. It gives a negative answer to Ye's problem (see [S. K. Ye, Low-dimensional representations of matrix group actions on CAT(0) spaces and manifolds, J. Algebra 409 (2014) 219-243]) for the above rings.",

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AB - We show that there is no nontrivial group homomorphism En(R) → En-1(R) over commutative local rings and division rings for n ≥ 3, respectively. It gives a negative answer to Ye's problem (see [S. K. Ye, Low-dimensional representations of matrix group actions on CAT(0) spaces and manifolds, J. Algebra 409 (2014) 219-243]) for the above rings.

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KW - division ring

KW - homomorphism

KW - local ring

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A note on the existence of nontrivial homomorphism e n (R) → e _n-1 (R)

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