Prescribed Gauss decompositions for Kac-Moody groups over fields
Rendiconti del Seminario Matematico della Università di Padova, Tome 106 (2001), pp. 153-163. 
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     author = {Morita, Jun and Plotkin, Eugene},
     title = {Prescribed {Gauss} decompositions for {Kac-Moody} groups over fields},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {153--163},
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}
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Morita, Jun; Plotkin, Eugene. Prescribed Gauss decompositions for Kac-Moody groups over fields. Rendiconti del Seminario Matematico della Università di Padova, Tome 106 (2001), pp. 153-163. http://www.numdam.org/item/RSMUP_2001__106__153_0/

[1] Z. Arad - M. Herzog, Products of conjugacy classes in groups, Lecture Notes in Mathematics, 1112, New York: Springer (1985). | MR | Zbl

[2] V. Chernousov - E.W. Ellers - N. Gordeev, Gauss decomposition with prescribed semisimple part: short proof, J. Algebra, 229 (2000), pp. 314-332. | MR | Zbl

[3] E.W. Ellers - N. GORDEEV, Gauss decompositions with prescribed semisimple part in classical Chevalley groups, Comm. Algebra, 14, 22 (1994), pp. 5935-5950. | MR | Zbl

[4] E.W. Ellers - N. GORDEEV, Gauss decompositions with prescribed semisimple part in Chevalley groups II Exceptional cases, Comm. Algebra, 8, 23 (1995), pp. 3085-3098. | MR | Zbl

[5] E.W. Ellers - N. GORDEEV, Gauss decompositions with prescribed semisimple part in Chevalley groups III: finite twisted groups, Comm. Algebra, 14, 24 (1996), pp. 4447-4475. | MR | Zbl

[6] E.W. Ellers - N. GORDEEV, On the conjectures of J. Thompson and O. Ore, Trans. Amer. Math. Soc., 9, 350 (2000), pp. 3657-3671. | MR | Zbl

[7] V.G. Kac, Infinite dimensional Lie algebras, Cambridge University Press (1990). | MR | Zbl

[8] V.G. Kac - D.H. Peterson, Defining relations of certain infinite-dimensional groups, in Proceedings of the Cartan conference, Astérisque, Numéro hors série (1985), pp. 165-208. | Numdam | MR | Zbl

[9] T. Laffey, Products of Matrices, in Generators and Relations in Groups and Geometries, Kluwer (1991), pp. 95-123. | MR | Zbl

[10] R.V. Moody - A. PIANZOLA, Lie algebras with triangular decompositions, John Wiley & Sons, New York (1995). | MR | Zbl

[11] J. Morita - E. PLOTKIN, Gauss decompositions of Kac-Moody groups, Comm. Algebra, 1, 27 (1999), pp. 465-475. | MR | Zbl

[12] O. Ore, Some remarks on commutators, Proc. AMS, 2 (1951), pp. 307-314. | MR | Zbl

[13] D.H. Peterson - V.G. Kac, Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci. USA, 80 (1983), pp. 1778-1782. | MR | Zbl

[14] R. Ree, Commutators in semi-simple algebraic groups, Proc. Amer. Math. Soc., 15 (1984), pp. 457-460. | MR | Zbl

[15] R. Steinberg, Lectures on Chevalley groups, Yale University, New Haven (1968). | MR

[16] A.R. Sourour, A factorization theorem for matrices, Linear and Multilinear Algebra, 19 (1986), pp. 141-147. | MR | Zbl

[17] J. Tits, Théorie de groupes, Résumé des cours et travaux 81e (1980- 1981), pp. 75-87, 82e (1981-1982), pp. 91-106, Collège de France, Paris.

[18] J. Tits, Groups and group functors attached to Kac-Moody data, Arbeitstagung, Bonn 1984, Springer Verlag Lect. Notes, 1111 (1985), 193-223. | MR | Zbl

[19] J. Tits, Uniqueness and Presentation Of Kac-Moody groups over fields, J. Algebra, 105 (1987), pp. 542-573. | MR | Zbl

[20] L. Vaserstein - E. Wheland, Commutators and companion matrices over rings of stable rank 1, Linear algebra and its applications, 142 (1990), pp. 263-277. | MR | Zbl