Toroidal groups¹Footnote

¹1991 AMS Classification: 20G20, 20E34, 19C09, 19C20, 17865, 17B10.

References

• Berman , S. and Moody , R.V. Lie algebras graded by finite root systems and the intersecfion matrix algebras of Slodowy, . invent.Math. , to appear
   Google Scholar
• Borcherds , R. 1986 . “ Proc. Natl. Acad. Sci ” . In Vertex algebras, Kac-Moody algebras and the Mouster Vol. 83 , 3068 – 3071 . USA
   Google Scholar
• Bourbaki , N. 1968 . “ Ch. IV, V, VI ” . In Groupes et algébres de Lie Hermann, , Paris
   Google Scholar
• Bourbaki , N. 1975 . “ Ch. VII, VIII ” . In Groupes et algébres de Lie Hermann, , Paris
   Google Scholar
• Carter , R.W. 1972 . Simple Groups of Lie Type Wiley, , London
   Google Scholar
• Chevalley , C. 1955 . Tohôku Math. J . Sur certains groupes simple , 7 ( 2 ) 14 – 66 .
   Google Scholar
• Chevalley , C. 1966 . Certains schémas de groupes semi-simples exposé 219, , New york "13e Séminairs N. Bourbaki, 1960-1961"
   Google Scholar
• Demazure , M. 1965 . Schémas en groupes réductifs 369 – 413 . France
   Google Scholar
• Eswara Rao , S. , Moody , R.V. and Yokonuma , T. Lie algebras arising from vertex operator representations , to appear
   Google Scholar
• Frenkel , I. and Kac , V. 1980 . Invent. Math . Basic representations of affine Lie algebras and dual resonance models , 62 : 23 – 66 .
   Google Scholar
• Frenkel , I. , Lepowsky , J. and Meurman , A. 1989 . Vertex operator algebras and the monster , Boston : Academic Press .
   Google Scholar
• Garland , H. 1980 . Publ. Math. IHES . The arithmetic theory of loop groups , 52 : 5 – 136 .
   Google Scholar
• Goddard , P. and Olive , D. 1984 . “ Publ. Math. Sci. Res. Inst ” . In Algebras, lattices and stringsVertex Operators in Mathematics and Physics , Vol. 3 , 51 – 96 . Springer-Verlag .
   Google Scholar
• Hahn , A. J and O'Meara , O.T. 1989 . The Classical Groups and K-theory , Berlin Heidelberg : Springer-Verlag .
   Google Scholar
• Hurrelbrink , J. 1977 . Math. Ann . Endlich präsentierte arithmetische Gruppen and K₂; über Laurent-Polynomringen , 225 123 – 129 .
   Google Scholar
• Kac , V. 1985 . Infinite Dimensional Lie Algebras , Cambridge University Press .
   Google Scholar
• Kac , V. and Peterson , D. 1983 . “ in "Arithmetic and Geometry", Progress in Math ” . In Regular functions on certain infinite groups Vol. 36 , 141 – 166 . Birkhäuser, , Boston
   Google Scholar
• Kac , V. and Peterson , D. 1983 . “ Proc. Natl. Acad. Sci ” . In Infinite flag varieties and conjugacy theorems Vol. 80 , 1778 – 1782 . USA
   Google Scholar
• van der Kallen , W. 1977 . Ann. Sci. Ecole. Sup . The K₂; of rings with many units , 10 ( 4 ) 473 – 515 .
   Google Scholar
• Kassel , C. 1984 . J. Pure and Applied Algebra . Kähler Differentials and coverings of complex simple Lie algebras extended over a commutative ring , 34 265 – 275 .
   Google Scholar
• Matsumoto , H. 1969 . Ann. Sci. Ec. Norm. Sup . Sur les sous-groupes arithmétiques des groupes , 2 ( 4 ) 1 – 62 .
   Google Scholar
• Milnor , J. “ Ann. Math. Stud ” . In Introduction to Algebraic K-theory , Vol. 72 , Princeton : Princeton University Press .
   Google Scholar
• Mitzman , D. Contemporary Mathematics (AMS) . Integral Bases for Affine Lie Algebras and Their , 40
   Google Scholar
• Moody , R. 1968 . A new class of Lie algebras . J. Algebra , 10 : 211 – 230 .
   Web of Science ®Google Scholar
• Moody , R.V. 1992 . Lie algebras with Traiangular Decomposition , J. Wiley .
   Google Scholar
• Moody , R. V. , Eswara Rao , S. and Yokonuma , T. 1990 . Geom. Ded . Toroidal Lie algebras and vertex repre¬sentations , 35 : 283 – 307 .
   Google Scholar
• Moody R.V. Shi Z. Toroidal Weyl groups to appear
   Google Scholar
• Moody , R.V. and Teo , K.L. 1972 . J. Algebra . Tits systems with crystallographic Weyl , 21 : 178 – 190 .
   Google Scholar
• Slodowy , P. 1986 . “ Can. Math. Soc. ” . In Beyond Kac-Moody algebras and inside Vol. 5 , 361 – 371 .
   Google Scholar
• Stein , M.R. 197 . Amer. J. Math. . Generators, relations and coverings of Chevalley , 93 : 965 – 1004 .
   Google Scholar
• 1962 . “ Théorie des Groupes Algébriques ” . In Générateurs, relations et 113 – 127 . Paris Bruxelles 1962
   Google Scholar
• Steinberg , R. 1967 . “ Yale Univ. Lecture Notes ” . In Lectures on Chevalley Groups notes by J. Faulkner and R.Wilson
   Google Scholar
• Tits , J. 1987 . J. Algebra . Uniqueness and presentation of Kac-Moody groups over fields , 105 : 542 – 573 .
   Google Scholar
• Tits , J. 1988-1989 . Séminaire Bourbaki 41eme année . Groupes associés aux algébres de Kac-Moody , 700
   Google Scholar