A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras
<p>Let <em>g</em> be a Kac–Moody algebra and <em>b</em><sub>1</sub>,<em>b</em><sub>2</sub> be Borel subalgebras of opposite signs. The intersection <em>b</em>=<em>b</em><sub>1</sub>∩<em>b</...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2007
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| _version_ | 1826289962425778176 |
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| author | Caprace, P |
| author_facet | Caprace, P |
| author_sort | Caprace, P |
| collection | OXFORD |
| description | <p>Let <em>g</em> be a Kac–Moody algebra and <em>b</em><sub>1</sub>,<em>b</em><sub>2</sub> be Borel subalgebras of opposite signs. The intersection <em>b</em>=<em>b</em><sub>1</sub>∩<em>b</em><sub>2</sub> is a finite-dimensional solvable subalgebra of <em>g</em>. We show that the nilpotency degree of [<em>b</em>,<em>b</em>] is bounded above by a constant depending only on <em>g</em>. This confirms a conjecture of Y. Billig and A. Pianzola [Y. Billig, A. Pianzola, Root strings with two consecutive real roots, Tohoku Math. J. (2) 47 (3) (1995) 391–403].</p> |
| first_indexed | 2024-03-07T02:36:54Z |
| format | Journal article |
| id | oxford-uuid:a918774f-d65f-4066-b736-3bf1642b1c10 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:36:54Z |
| publishDate | 2007 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:a918774f-d65f-4066-b736-3bf1642b1c102022-03-27T03:06:04ZA uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a918774f-d65f-4066-b736-3bf1642b1c10MathematicsEnglishOxford University Research Archive - ValetElsevier2007Caprace, P<p>Let <em>g</em> be a Kac–Moody algebra and <em>b</em><sub>1</sub>,<em>b</em><sub>2</sub> be Borel subalgebras of opposite signs. The intersection <em>b</em>=<em>b</em><sub>1</sub>∩<em>b</em><sub>2</sub> is a finite-dimensional solvable subalgebra of <em>g</em>. We show that the nilpotency degree of [<em>b</em>,<em>b</em>] is bounded above by a constant depending only on <em>g</em>. This confirms a conjecture of Y. Billig and A. Pianzola [Y. Billig, A. Pianzola, Root strings with two consecutive real roots, Tohoku Math. J. (2) 47 (3) (1995) 391–403].</p> |
| spellingShingle | Mathematics Caprace, P A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras |
| title | A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras |
| title_full | A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras |
| title_fullStr | A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras |
| title_full_unstemmed | A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras |
| title_short | A uniform bound on the nilpotency degree of certain subalgebras of Kac–Moody algebras |
| title_sort | uniform bound on the nilpotency degree of certain subalgebras of kac moody algebras |
| topic | Mathematics |
| work_keys_str_mv | AT capracep auniformboundonthenilpotencydegreeofcertainsubalgebrasofkacmoodyalgebras AT capracep uniformboundonthenilpotencydegreeofcertainsubalgebrasofkacmoodyalgebras |