Geodesic
CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS
Glasgow mathematical journal, Tome 62 (2020), pp. S14-S27

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

The exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$-structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras. 
CUNHA, ISABEL; ELDUQUE, ALBERTO. CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS. Glasgow mathematical journal, Tome 62 (2020), pp. S14-S27. doi: 10.1017/S0017089519000181
@article{10_1017_S0017089519000181,
     author = {CUNHA, ISABEL and ELDUQUE, ALBERTO},
     title = {CODES, {S-STRUCTURES,} {AND} {EXCEPTIONAL} {LIE} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {S14--S27},
     year = {2020},
     volume = {62},
     number = {S1},
     doi = {10.1017/S0017089519000181},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000181/}
}
TY  - JOUR
AU  - CUNHA, ISABEL
AU  - ELDUQUE, ALBERTO
TI  - CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2020
SP  - S14
EP  - S27
VL  - 62
IS  - S1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000181/
DO  - 10.1017/S0017089519000181
ID  - 10_1017_S0017089519000181
ER  - 
%0 Journal Article
%A CUNHA, ISABEL
%A ELDUQUE, ALBERTO
%T CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS
%J Glasgow mathematical journal
%D 2020
%P S14-S27
%V 62
%N S1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000181/
%R 10.1017/S0017089519000181
%F 10_1017_S0017089519000181

[1] Allison, B., Benkart, G. and Gao, Y., Lie algebras graded by the root systems BC , r ≥ 2, Memoirs of the American Mathematical Society, vol. 751 (American Mathematical Society, 2002). Google Scholar

[2] Benkart, G. and Elduque, A., Lie algebras with prescribed decomposition, Proc. Am. Math. Soc. 140(8) (2012), 2627–2638. Google Scholar | DOI

[3] Bermann, S. and Moody, R. V., Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy, Invent. Math. 108(2) (1992), 323–347. Google Scholar | DOI

[4] Bourbaki, N., Lie groups and Lie algebras. Chapters 4–6, Elements of Mathematics (Springer-Verlag, Berlin, 2002). Google Scholar | DOI

[5] Bourbaki, N., Lie groups and Lie algebras. Chapters 7–9, Elements of Mathematics (Springer-Verlag, Berlin, 2005). Google Scholar

[6] Castillo-Ramrez, A., Mcinroy, J. and Rehren, F., Code algebras, axial algebras and VOAs, J. Algebra 518 (2019), 146–176. Google Scholar | DOI

[7] Conway, J. H. and Sloane, N. J. A., Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften, vol. 290, 3rd edition, (Springer-Verlag, New York, 1999). Google Scholar | DOI

[8] Ebeling, W., Lattices and codes, in A course partially based on lectures (Hirzebruch, F., Editor), Advanced Lectures in Mathematics (Friedr. Vieweg & Sohn, Braunschweig, 1994). Google Scholar

[9] Elduque, A., The magic square and symmetric compositions. II, Rev. Mat. Iberoam. 23(1) (2007), 57–84. Google Scholar | DOI

[10] Elduque, A. and Kochetov, M., Gradings on simple Lie algebras, Mathematical Surveys and Monographs, vol. 189 (American Mathematical Society, Providence, RI, 2013). Google Scholar

[11] Vinberg, E. B., Non-abelian gradings of Lie algebras, in 50th Seminar “Sophus Lie”, vol. 113 (Banach Center Publ., Polish Acad. Sci. Inst. Math., Warsaw, 2017), 19–38. Google Scholar

Cité par Sources :