Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T06:41:50.510Z Has data issue: false hasContentIssue false

Central Quotients and Coverings of Steinberg Unitary Lie Algebras

Published online by Cambridge University Press:  20 November 2018

Bruce N. Allison
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, AB T6G 2G1 email: e-mail: [email protected]: [email protected]
Yun Gao
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, AB T6G 2G1 email: e-mail: [email protected]: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we calculate the center and the universal covering algebra of the Steinberg unitary Lie algebra stun, where is a unital nonassociative algebra with involution and n ≥ 3.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1996

References

[A1] Allison, B.N., A class ofnonassociative algebras with involution containing the class of Jordan algebras, Math. Ann. 237 (1978), 133156.Google Scholar
[A2] Allison, B.N., Construction of 3 x 3 matrix Lie algebras and some Lie algebras of type D4, J.Algebra 143( 1991),6392.Google Scholar
[AF] Allison, B.N. and Faulkner, J.R., Nonassociative coefficient algebras for Steinberg unitary Lie algebras, J.Algebra 161 (1993), 119.Google Scholar
[AY] Asano, H. and Yamaguti, K., A construction of Lie algebras by generalized Jordan triples systems of second order, Indag. Math. (N.S.) 42 (1980), 249253.Google Scholar
[BGKN] Berman, S., Gao, Y., Krylyuk, Y., Neher, E., The alternative torus and the structure of elliptic quasisimple Lie algebras of type A2, Trans. Amer. Math. Soc, 347 (1995), 43154363.Google Scholar
[F] Faulkner, J.R., Structurable triples, Lie triples, and symmetric spaces, Forum Math., 6 (1994), 637650.Google Scholar
[G] Gao, Y., Steinberg unitary Lie algebras and skew-dihedral homology, J.Algebra, 179 (1996), 261304.Google Scholar
[Ga] Garland, H., The arithmetic theory of loop groups, Publ. Math. IHES 52 (1980), 5136.Google Scholar
[J] Jacobson, N., Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ. 39 (1968).Google Scholar
[K] Kantor, I.L., Some generalizations of Jordan algebas, Trudy Sem. Vektor. Tenzor. Anal. 16 (1972), 407499.Google Scholar
[KL] Kassel, C. and Loday, J.-L., Extensions centrales d'algebres de Lie, Ann. Inst. Fourier (Grenoble) 32 (1982), 119142.Google Scholar
[KLS] Krasauskas, R.L., Lapin, S.V. and Solovev, Yu. P., Dihedral homology and cohomology, Basic notions and constructions, Math. USSR-Sb. 133 (1987), 2548.Google Scholar
[L] Loday, J.-L., Homologies diedrale et quaternionique, Adv. in Math. (China) 66 (1987), 119148.Google Scholar
[Se] Seligman, G.B., Constructions of Lie algebras and their modules, Lect. Notes in Math., Springer- Verlag, New York 1300 (1988).Google Scholar
[Sh] Schafer, R.D., On structurable algebras, J.Algebra 92 (1985), 400412.Google Scholar
[Sm] Smirnov, O.N., Simple and semisimple structurable algebras, Algebra and Logic 29 (1990), 377394.Google Scholar