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The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras

Published online by Cambridge University Press:  20 November 2018

Maribel Tocón
Maribel Tocón*
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5 e-mail: maribel@uma.es
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Abstract

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In this paper we prove that the Kostrikin radical of an extended affine Lie algebra of reduced type coincides with the center of its core, and use this characterization to get a type-free description of the core of such algebras. As a consequence we get that the core of an extended affine Lie algebra of reduced type is invariant under the automorphisms of the algebra.

Keywords

17B0517B65extended affine Lie algebraLie toruscoreKostrikin radical
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 298 - 309
Copyright
Copyright © Canadian Mathematical Society 2008

References

[AABGP] Allison, B., Azam, S., Berman, S., Gao, Y., and Pianzola, A., Extended affine Lie algebras and their root systems. Mem. Amer. Math. Soc. 126(1997), no. 603.Google Scholar
[AFY] Allison, B., Faulkner, J., and Yoshii, Y., Lie tori of rank 1. Resenhaus, 6(2004), no. 2–3, 99–109.Google Scholar
[AG] Allison, B. and Gao, Y., The root systems and the core of an extended affine Lie algebra. Selecta Math. (N.S.) 7(2001), no. 2, 149–212.Google Scholar
[AY] Allison, B. and Yoshii, Y., Structurable tori and extended affine Lie algebras of type BC 1 . J. Pure Appl. Algebra 184(2003), no. 2–3, 105–138.Google Scholar
[BGK] Berman, S., Gao, Y., and Krylyuk, Y., Quantum tori and the structure of elliptic quasi-simple Lie algebras. J. Funct. Anal. 135(1996), 339–389.Google Scholar
[BGKN] Berman, S., Gao, Y., Krylyuk, Y., and Neher, E., The alternative torus and the structure of elliptic quasi-simple Lie algebras of type A 2 . Trans. Amer. Math. Soc. 347(1995), no. 11, 4315–4363.Google Scholar
[F] Faulkner, J., lie tori of type BC 2 and structurable quasitori. To appear in Comm. Algebra.Google Scholar
[Fi] Filippov, V. T., On nil-elements of index 2 in Mat’tsev algebras. deposited at the All-Union Institute for Scientific and Technical Information (VINITI), 2499-80 (1986).Google Scholar
[HT] Hoegh-Krohn, R. and Torrésani, B., Classification and construction of quasi-simple Lie algebras. J. Funct. Anal. 89(1990), no. 1, 106–136.Google Scholar
[K] Kostrikin, A. I., Sandwiches in Lie algebras. Math. Sb. 110(152)(1979), no. 1, 3–12, 159.Google Scholar
[K2] Kostrikin, A. I., Around Burnside. Ergebnisse der Mathematik und ihrer Grenzgebiete 3, Springer-Verlag, Berlin, 1990.Google Scholar
[Kr] Krylyuk, Y., On automorphisms and isomorphisms of quasi-simple Lie algebras. J. Math. Sci. 100(2000), no. 1, 1944–2002.Google Scholar
[LN] Loos, O. and Neher, E., Locally finite root systems. Mem. Amer. Math. Soc. 171(2004) no. 811.Google Scholar
[N] Neher, E., Lie tori. C. R. Math. Acad. Sci. Soc. R. Can. 26(2004), no. 3, 84–89.Google Scholar
[N2] Neher, E., Extended affine Lie algebras. C. R. Math. Acad. Sci. Soc. R. Can. 26(2004), no. 3, 90–96.Google Scholar
[S] Strade, H., Simple Lie Algebras over Fields of Positive Characteristic. I. Structure Theory. de Gruyter Expositions in Mathematics 38, Walter de Gruyter, Berlin, 2004.Google Scholar
[Y] Yoshii, Y., Coordinate algebras of extended affine Lie algebras of type A 1 . J. Algebra 234(2000), no. 1, 128–168.Google Scholar
[Y2] Yoshii, Y., Root-graded Lie algebras with compatible gradings. Comm. Algebra 29(2001), no. 8, 3365–3391.Google Scholar
[Y3] Yoshii, Y., Lie tori—A simple characterization of extended affine Lie algebras. Publ. Res. Inst. Math. Sci. 42(2006), no. 3, 739–762.Google Scholar
[Yo] Yousofzadeh, M., A generalization of EALA. arXiv:math.QA/0702070Google Scholar
[Z] Zelmanov, E. I., Lie algebras with an algebraic adjoint representation. Math. Sb. 121(163)(1983), no. 4, 545–561.Google Scholar