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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 3, Pages 540–547
(Mi smj1860)
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This article is cited in 12 scientific papers (total in 12 papers)
Conformal representations of Leibniz algebras
P. S. Kolesnikov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We study the embedding construction of Lie dialgebras (Leibniz algebras) into conformal algebras. This construction leads to the concept of a conformal representation of Leibniz algebras. We prove that each (finite-dimensional) Leibniz algebra possesses a faithful linear representation (of finite type). As a corollary we give a new proof of the Poincaré–Birkhoff–Witt theorem for Leibniz algebras.
Keywords:
Leibniz algebra, dialgebra, conformal algebra.
Received: 14.08.2007
Citation:
P. S. Kolesnikov, “Conformal representations of Leibniz algebras”, Sibirsk. Mat. Zh., 49:3 (2008), 540–547; Siberian Math. J., 49:3 (2008), 429–435
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https://www.mathnet.ru/eng/smj1860 https://www.mathnet.ru/eng/smj/v49/i3/p540
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Abstract page: | 383 | Full-text PDF : | 131 | References: | 39 |
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