Characters of the group $\mathrm{EL}_d (R)$ for a commutative Noetherian ring $R$

Omer Lavi; Arie Levit

Characters of the group $\mathrm{EL}_d (R)$ for a commutative Noetherian ring $R$

Group Theory 2020-07-31 v1 Rings and Algebras Representation Theory

Authors: Omer Lavi , Arie Levit

Abstract

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

Keywords

commutative Noetherian ring elementary linear group characters stable range invariant measures Pontryagin dual

Cite

@article{arxiv.2007.15547,
  title  = {Characters of the group $\mathrm{EL}_d (R)$ for a commutative Noetherian ring $R$},
  author = {Omer Lavi and Arie Levit},
  journal= {arXiv preprint arXiv:2007.15547},
  year   = {2020}
}

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51 pages

Characters of the group $\mathrm{EL}_d (R)$ for a commutative Noetherian ring $R$

Abstract

Keywords

Cite

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