Faithful representations of Leibniz algebras

Faithful representations of Leibniz algebras
HTML articles powered by AMS MathViewer

by Donald W. Barnes PDF

Proc. Amer. Math. Soc. 141 (2013), 2991-2995 Request permission

Let $L$ be a Leibniz algebra of dimension $n$. We prove the existence of a faithful $L$-module of dimension less than or equal to $n+1$.

References

Sh. A. Ayupov and B. A. Omirov, On Leibniz algebras, Algebra and operator theory (Tashkent, 1997) Kluwer Acad. Publ., Dordrecht, 1998, pp. 1–12. MR 1643399
Donald W. Barnes, Ado-Iwasawa extras, J. Aust. Math. Soc. 78 (2005), no. 3, 407–421. MR 2142164, DOI 10.1017/S1446788700008600
D. W. Barnes, Schunck classes of soluble Leibniz algebras, arXiv:1101.3046 (2011). To appear in Comm. Algebra.
Donald W. Barnes and Humphrey M. Gastineau-Hills, On the theory of soluble Lie algebras, Math. Z. 106 (1968), 343–354. MR 232807, DOI 10.1007/BF01115083
G. Hochschild, An addition to Ado’s theorem, Proc. Amer. Math. Soc. 17 (1966), 531–533. MR 194482, DOI 10.1090/S0002-9939-1966-0194482-0
Kenkichi Iwasawa, On the representation of Lie algebras, Jpn. J. Math. 19 (1948), 405–426. MR 32613
Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
Jean-Louis Loday and Teimuraz Pirashvili, Leibniz representations of Lie algebras, J. Algebra 181 (1996), no. 2, 414–425. MR 1383474, DOI 10.1006/jabr.1996.0127
Alexandros Patsourakos, On nilpotent properties of Leibniz algebras, Comm. Algebra 35 (2007), no. 12, 3828–3834. MR 2371257, DOI 10.1080/00927870701509099