Inner automorphisms of Lie algebras related with generic 2 × 2 matrices
Let Fm = Fm(var(sl₂(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl₂(K) over a field K of characteristic 0. Translating an old result of Baker from 1901 we present a multiplication rule for the inner automorphisms of the completion Fmˆ of Fm w...
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| Datum: | 2012 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2012
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/152228 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Inner automorphisms of Lie algebras related with generic 2 × 2 matrices / V. Drensky, S. Fındık // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 49-70. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let Fm = Fm(var(sl₂(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl₂(K) over a field K of characteristic 0. Translating an old result of Baker from 1901 we present a multiplication rule for the inner automorphisms of the completion Fmˆ of Fm with respect to the formal power series topology. Our results are more precise for m = 2 when F₂ is isomorphic to the Lie algebra L generated by two generic traceless 2×2 matrices. We give a complete description of the group of inner automorphisms of Lˆ. As a consequence we obtain similar results for the automorphisms of the relatively free algebra Fm / Fm c⁺¹ = Fm(var(sl₂(K)) ∩ Nc) |
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