Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type
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 $\Omega_G$...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1826282320282255360 |
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| author | Ardakov, K Wei, F Zhang, J |
| author_facet | Ardakov, K Wei, F Zhang, J |
| author_sort | Ardakov, K |
| collection | OXFORD |
| description | 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 $A_1$. |
| first_indexed | 2024-03-07T00:42:04Z |
| format | Journal article |
| id | oxford-uuid:836181dc-8551-445f-9197-bed0c13fb39e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:42:04Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:836181dc-8551-445f-9197-bed0c13fb39e2022-03-26T21:43:49ZNonexistence of reflexive ideals in Iwasawa algebras of Chevalley typeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:836181dc-8551-445f-9197-bed0c13fb39eEnglishSymplectic Elements at Oxford2007Ardakov, KWei, FZhang, JLet $\Phi$ 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 $A_1$. |
| spellingShingle | Ardakov, K Wei, F Zhang, J Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type |
| title | Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type |
| title_full | Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type |
| title_fullStr | Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type |
| title_full_unstemmed | Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type |
| title_short | Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type |
| title_sort | nonexistence of reflexive ideals in iwasawa algebras of chevalley type |
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