Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Buildings as inner ideal geometries


Author: Meighan I. Dillon
Journal: Proc. Amer. Math. Soc. 123 (1995), 647-650
MSC: Primary 20E42; Secondary 17B67, 51B25
DOI: https://doi.org/10.1090/S0002-9939-1995-1264806-X
MathSciNet review: 1264806
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a Chevalley-type group $ G(V)$ associated to an integrable representation of a Kac-Moody algebra and show that the associated Kac-Moody group $ G(A)$ is a universal cover for $ G(V)$. This observation strengthens a result of Kac-Peterson on representations of $ G(A)$. It also implies that the building associated to an affine Lie algebra can be realized as an inner ideal geometry.


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Groupes et algèbres de Lie, Chs. IV-VI, Hermann, Paris, 1968. MR 0240238 (39:1590)
  • [2] K. Brown, Buildings, Springer-Verlag, New York, 1989. MR 969123 (90e:20001)
  • [3] M. Dillon, Geometry and affine Lie algebras, J. Algebra 135 (1990), 96-111. MR 1076079 (92b:17039)
  • [4] V. Kac, Infinite dimensional Lie algebras, Progr. Math., vol. 44, Birkhäuser, Boston, 1983. MR 739850 (86h:17015)
  • [5] V. G. Kac and D. H. Peterson, Defining relations of certain infinite-dimensional groups, Élie Cartan et les Mathématiques d'aujourd'hui, vol. hors série, Astérisque, 1985, pp. 165-208. MR 837201 (87j:22027)
  • [6] -, On geometric invariant theory for infinite-dimensional groups, Algebraic Groups, Utrecht 1986, Lecture Notes in Math., vol. 1271, Springer-Verlag, New York, 1987, pp. 109-142. MR 911137 (89b:22028)
  • [7] -, Regular functions on certain infinite-dimensional groups, Arithmetic and Geometry, Progr. Math., vol 36, Birkhäuser, Boston, 1983, pp. 141-166. MR 717610 (86b:17010)
  • [8] D. H. Peterson and V. G. Kac, Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci. U.S.A. 80 (1983), 1778-1782. MR 699439 (84g:17017)
  • [9] M. Ronan, Lectures on buildings, Perspect. Math., vol. 7, Academic Press, San Diego, 1989. MR 1005533 (90j:20001)
  • [10] R. Steinberg, Lecture notes on Chevalley groups, Yale University Lecture Notes, 1967.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E42, 17B67, 51B25

Retrieve articles in all journals with MSC: 20E42, 17B67, 51B25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1264806-X
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society