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Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

Abstract:
Let $\Phi$ be a root system and let $\Phi(\Zp)$ be the standard Chevalley $\Zp$-Lie algebra associated to $\Phi$. For any integer $t\geq 1$, let $G$ be the uniform pro-$p$ group corresponding to the powerful Lie algebra $p^t \Phi(\Zp)$ and suppose that $p\geq 5$. Then the Iwasawa algebra $\Omega_G$ has no nontrivial reflexive two-sided ideals. This was previously proved by the authors for the root system $A_1$.

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
Journal of Algebra
Volume:
320
Issue:
1
Pages:
259-275
Publication date:
2007-10-02
DOI:
EISSN:
1090-266X
ISSN:
0021-8693
URN:
uuid:836181dc-8551-445f-9197-bed0c13fb39e
Source identifiers:
399417
Local pid:
pubs:399417
Language:
English
Keywords:

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