Geodesic
On Some Twisted Chevalley Groups Over Laurent Polynomial Rings
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1182-1201

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

We let Z denote the ring of rational integers, Q the field of rational numbers, R the field of real numbers, and C the field of complex numbers.For elements e and f of a Lie algebra, [e,f] denotes the bracket of e and f. A generalized Cartan matrix C = (cij ) is a square matrix of integers satisfying cii = 2, cij ≦ 0 if i ≠ j, cij = 0 if and only if cji = 0. For any generalized Cartan matrix C = (cij ) of size l × l and for any field F of characteristic zero, denotes the Lie algebra over F generated by 3l generators e 1, ..., el , h 1, ..., hl , f 1, ..., fl with the defining relations for all i, j, for distinct i, j. 
Morita, Jun. On Some Twisted Chevalley Groups Over Laurent Polynomial Rings. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1182-1201. doi: 10.4153/CJM-1981-089-6
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[1] 1. Abe, E., Coverings of twisted Chevalley groups over commutative rings, Sci. Rep. Tōkyō Kyōiku Daigaku 13 (1977), 194–218. Google Scholar

[2] 2. Bourbaki, N., Groupes et algèbres de Lie, Chap. 4-6 (Hermann, Paris, 1968). Google Scholar

[3] 3. Humphreys, J. E., Introduction to Lie algebras and representation theory, (Springer, Berlin, 1972). Google Scholar

[4] 4. Iwahori, N., On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci., Univ. of Tokyo 10 (1964), 215–236. Google Scholar

[5] 5. Kac, V. G., Simple irreducible graded Lie algebras of finite growth, Math. USSR-Izvestija 2 (1968), 1271–1311. Google Scholar

[6] 6. Kac, V. G., Automorphisms of finite order of semisimple Lie algebras, Functional Anal. Appl. 3 (1969), 252–254. Google Scholar

[7] 7. Macdonald, I. G., Affine root systems and Dedekind's η-functions, Inventiones Math. 15 (1972), 91–143. Google Scholar

[8] 8. Moody, R. V., Euclidean Lie algebras, Can. J. Math. 21 (1969), 1432–1454. Google Scholar

[9] 9. Moody, R. V., Simple quotients oj'Euclidean Lie algebras, Can. J. Math. 22 (1970), 839–846. Google Scholar

[10] 10. Moody, R. V. and Teo, K. L., Tits’ systems with crystallo graphic Weyl groups, J. Algebra 21 (1972), 178–190. Google Scholar

[11] 11. Morita, J., Tits1 systems in Chevalley groups over Laurent polynomial rings, Tsukuba J. Math. 3 (1979), 41–51. Google Scholar

[12] 12. Steinberg, R., Lectures on Chevalley groups, Yale Univ. Lecture Notes (1967/68). Google Scholar

[13] 13. Teo, K. L., Simple quotients of the three tiered Euclidean Lie algebra, Bull. London Math. Soc. 9 (1977), 299–304. Google Scholar

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