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

^*Corresponding author for this work

School of Mathematics and Statistics

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

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	259-275
Number of pages	17
Journal	Journal of Algebra
Volume	320
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2007.12.020
Publication status	Published - 1 Jul 2008

Keywords

Chevalley type
Iwasawa algebra
Reflexive ideal

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10.1016/j.jalgebra.2007.12.020

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title = "Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type",

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 - Ardakov, K.

AU - Wei, F.

AU - Zhang, J. J.

PY - 2008/7/1

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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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SP - 259

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JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

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

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Keywords

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