Central Quotients and Coverings of Steinberg Unitary Lie Algebras
Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 449-482

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1996-023-6
Mots-clés : 17B60, 19D55, 17B55
Allison, Bruce N.; Gao, Yun. Central Quotients and Coverings of Steinberg Unitary Lie Algebras. Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 449-482. doi: 10.4153/CJM-1996-023-6
@article{10_4153_CJM_1996_023_6,
     author = {Allison, Bruce N. and Gao, Yun},
     title = {Central {Quotients} and {Coverings} of {Steinberg} {Unitary} {Lie} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {449--482},
     year = {1996},
     volume = {48},
     number = {3},
     doi = {10.4153/CJM-1996-023-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-023-6/}
}
TY  - JOUR
AU  - Allison, Bruce N.
AU  - Gao, Yun
TI  - Central Quotients and Coverings of Steinberg Unitary Lie Algebras
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 449
EP  - 482
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-023-6/
DO  - 10.4153/CJM-1996-023-6
ID  - 10_4153_CJM_1996_023_6
ER  - 
%0 Journal Article
%A Allison, Bruce N.
%A Gao, Yun
%T Central Quotients and Coverings of Steinberg Unitary Lie Algebras
%J Canadian journal of mathematics
%D 1996
%P 449-482
%V 48
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-023-6/
%R 10.4153/CJM-1996-023-6
%F 10_4153_CJM_1996_023_6

[A1] Allison, B.N., A class ofnonassociative algebras with involution containing the class of Jordan algebras, Math. Ann. 237 (1978), 133–156. 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),63–92. Google Scholar

[AF] Allison, B.N. and Faulkner, J.R., Nonassociative coefficient algebras for Steinberg unitary Lie algebras, J.Algebra 161 (1993), 1–19. 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), 249–253. 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), 4315–4363. Google Scholar

[F] Faulkner, J.R., Structurable triples, Lie triples, and symmetric spaces, Forum Math., 6 (1994), 637–650. Google Scholar

[G] Gao, Y., Steinberg unitary Lie algebras and skew-dihedral homology, J.Algebra, 179 (1996), 261–304. Google Scholar

[Ga] Garland, H., The arithmetic theory of loop groups, Publ. Math. IHES 52 (1980), 5–136. 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), 407–499. Google Scholar

[KL] Kassel, C. and Loday, J.-L., Extensions centrales d'algebres de Lie, Ann. Inst. Fourier (Grenoble) 32 (1982), 119–142. 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), 25–48. Google Scholar

[L] Loday, J.-L., Homologies diedrale et quaternionique, Adv. in Math. (China) 66 (1987), 119–148. 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), 400–412. Google Scholar

[Sm] Smirnov, O.N., Simple and semisimple structurable algebras, Algebra and Logic 29 (1990), 377–394. Google Scholar

Cité par Sources :