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

Omer Lavi; Arie Levit

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arXiv · 2007.15547

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

Omer Lavi·Arie Levit

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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 $R^d$.

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Omer Lavi, Arie Levit. 2020-07-30. Characters of the group $\mathrm{EL}_d (R)$ for a commutative Noetherian ring $R$. https://arxiv.org/abs/2007.15547

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