Geodesic
Outer Derivations and Classical-Albert-Zassenhaus lie Algebras
Canadian journal of mathematics, Tome 36 (1984) no. 6, pp. 961-972

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

This paper is concerned with the structure of the derivation algebra Der L of the Lie algebra L with split Cartan subalgebra H. The Fitting decomposition of Der L with respect to ad ad H leads to a decomposition where This decomposition is studied in detail in Section 2, where the centralizer of ad L∞ in D 0(H) is shown to be which is Hom(L/L 2, Center L) when H is Abelian. When the root-spaces La (a nonzero) are one-dimensional, this leads to the decomposition of Der L as where T is any maximal torus of D 0(H). 
Winter, David J. Outer Derivations and Classical-Albert-Zassenhaus lie Algebras. Canadian journal of mathematics, Tome 36 (1984) no. 6, pp. 961-972. doi: 10.4153/CJM-1984-054-7
@article{10_4153_CJM_1984_054_7,
     author = {Winter, David J.},
     title = {Outer {Derivations} and {Classical-Albert-Zassenhaus} lie {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {961--972},
     year = {1984},
     volume = {36},
     number = {6},
     doi = {10.4153/CJM-1984-054-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1984-054-7/}
}
TY  - JOUR
AU  - Winter, David J.
TI  - Outer Derivations and Classical-Albert-Zassenhaus lie Algebras
JO  - Canadian journal of mathematics
PY  - 1984
SP  - 961
EP  - 972
VL  - 36
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1984-054-7/
DO  - 10.4153/CJM-1984-054-7
ID  - 10_4153_CJM_1984_054_7
ER  - 
%0 Journal Article
%A Winter, David J.
%T Outer Derivations and Classical-Albert-Zassenhaus lie Algebras
%J Canadian journal of mathematics
%D 1984
%P 961-972
%V 36
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1984-054-7/
%R 10.4153/CJM-1984-054-7
%F 10_4153_CJM_1984_054_7

[1] 1. Albert, A. A. and Frank, M. S., Simple Lie algebras of characteristic p, Univ. e Politec. Torino, Rend. Sem. Mat. 14 (1954-5), 117–139. Google Scholar

[2] 2. Block, R., On Lie algebras of rank 1, Trans. A.M.S. 112 (1964), 19–31. Google Scholar

[3] 3. Block, R., On the Mills-Seligman axioms for Lie algebras of classical type, Trans. A.M.S. Soc. 121 (1966), 378–392. Google Scholar

[4] 4. Block, R., Trace forms in Lie algebras, Can. J. Math. 14 (1962), 553–564. Google Scholar

[5] 5. Mills, W., Classical type Lie algebras of characteristics 5 and 7, J. Math. Mech. 6 (1957), 559–566. Google Scholar

[6] 6. Mills, W. and Seligman, G., Lie algebras of classical type, J. Math. Mech. 6 (1957), 519–548. Google Scholar

[7] 7. Schenkman, E., A theory of subinvariant Lie algebras, Am. J. Math. 173 (1951), 453–474. Google Scholar

[8] 8. Seligman, G., Modular Lie algebras, Ergebnisse der Math. u. ihrer Grenzegebiete Bd. 40 (Springer-Verlag, Berlin, 1967). Google Scholar | DOI

[9] 9. Winter, D. J., On the toral structure of Lie p-algebras, Acta Math. 123 (1969), 70–81. Google Scholar

[10] 10. Winter, D. J., Symmetric Lie algebras. Google Scholar | DOI

[11] 11. Winter, D. J., Symmetrysets, J. of Alg. 73 (1981), 238–247. Google Scholar

Cité par Sources :