Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type

K. Ardakov; F. Wei; J. J. Zhang

doi:10.1016/j.jalgebra.2007.12.020

Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type

K. Ardakov^*, F. Wei, J. J. Zhang

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

Let Φ be a root system and let Φ (Z_p) be the standard Chevalley Z_p-Lie algebra associated to Φ. For any integer t ≥ 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra p^t Φ (Z_p) and suppose that p ≥ 5. Then the Iwasawa algebra Ω_G has no non-trivial two-sided reflexive ideals. This was previously proved by the authors for the root system A₁.

源语言	英语
页（从-至）	259-275
页数	17
期刊	Journal of Algebra
卷	320
期	1
DOI	https://doi.org/10.1016/j.jalgebra.2007.12.020
出版状态	已出版 - 1 7月 2008

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10.1016/j.jalgebra.2007.12.020

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abstract = "Let Φ be a root system and let Φ (Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t ≥ 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra pt Φ (Zp) and suppose that p ≥ 5. Then the Iwasawa algebra ΩG has no non-trivial two-sided reflexive ideals. This was previously proved by the authors for the root system A1.",

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AU - Wei, F.

AU - Zhang, J. J.

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N2 - Let Φ be a root system and let Φ (Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t ≥ 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra pt Φ (Zp) and suppose that p ≥ 5. Then the Iwasawa algebra ΩG has no non-trivial two-sided reflexive ideals. This was previously proved by the authors for the root system A1.

AB - Let Φ be a root system and let Φ (Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t ≥ 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra pt Φ (Zp) and suppose that p ≥ 5. Then the Iwasawa algebra ΩG has no non-trivial two-sided reflexive ideals. This was previously proved by the authors for the root system A1.

KW - Chevalley type

KW - Iwasawa algebra

KW - Reflexive ideal

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Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type

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