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Inner automorphisms of Lie algebras related with generic 2 × 2 matrices
Репозиторій DSpace/Manakin
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Inner automorphisms of Lie algebras related with generic 2 × 2 matrices
Інший ID:
2010 MSC:17B01, 17B30, 17B40, 16R30.
Посилання:
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.
Підтримка:
The research of the first author was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the second author was partially supported by the Council of Higher Education (YÖK) in Turkey. The second named author is grateful to the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences for the creative atmosphere and the warm hospitality during his visit when most of this project was carried out.
Дата:
2012
Переглядів:
414
Завантажень:
161
Анотація:
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)
