Characters of the group ELd(R) for a commutative Noetherian ring R

Omer Lavi; Arie Levit

doi:10.1016/j.aim.2023.108948

Characters of the group EL_d(R) for a commutative Noetherian ring R

Omer Lavi, Arie Levit^*

^*Corresponding author for this work

School of Mathematical Sciences

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

1 Scopus citations

Abstract

Let R be a commutative Noetherian ring with unit. We classify the characters of the group EL_d(R) provided that d is greater than the stable range of the ring R. It follows that every character of EL_d(R) is induced from a finite dimensional representation. Towards our main result we classify EL_d(R)-invariant probability measures on the Pontryagin dual group of R^d.

Original language	English
Article number	108948
Journal	Advances in Mathematics
Volume	419
DOIs	https://doi.org/10.1016/j.aim.2023.108948
State	Published - 15 Apr 2023

Keywords

Character rigidity
Characters
Elementary matrices
Noetherian rings
Universal lattices

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10.1016/j.aim.2023.108948

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abstract = "Let R be a commutative Noetherian ring with unit. We classify the characters of the group ELd(R) provided that d is greater than the stable range of the ring R. It follows that every character of ELd(R) is induced from a finite dimensional representation. Towards our main result we classify ELd(R)-invariant probability measures on the Pontryagin dual group of Rd.",

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AB - Let R be a commutative Noetherian ring with unit. We classify the characters of the group ELd(R) provided that d is greater than the stable range of the ring R. It follows that every character of ELd(R) is induced from a finite dimensional representation. Towards our main result we classify ELd(R)-invariant probability measures on the Pontryagin dual group of Rd.

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KW - Characters

KW - Elementary matrices

KW - Noetherian rings

KW - Universal lattices

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Characters of the group EL_d(R) for a commutative Noetherian ring R

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Keywords

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