Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T06:08:00.973Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniqueness theorems for left-symmetric enveloping algebras

Published online by Cambridge University Press:  24 October 2008

J. R. Bolgar
J. R. Bolgar
Affiliation:
Department of Mathematical Sciences, Goldsmiths' College, University of London, New Cross, London SE14 6NW e-mail [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Let L be a Lie algebra over a field of characteristic zero. We study the uni versai left-symmetric enveloping algebra U(L) introduced Dan Segal in [9]. We prove some uniqueness results for these algebras and determine their automorphism groups, both as left-symmetric algebras and as Lie algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 2 , August 1996 , pp. 193 - 206
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Benoist, Y.. Une nilvariété non affine. C. R. Acad. Sci. Sér. I, 315 (1992), 983–986.Google Scholar
[2]Burde, D. and Grunewald, F.. Modules for certain Lie algebras of maximal class (preprint).Google Scholar
[3]Kim, H.. Complete left-invariant affine structures on nilpotent Lie groups. Journal of Differential Geometry 24 (1986), 373–394.CrossRefGoogle Scholar
[4]Fried, D., Goldman, W. and Hirsch, M.. Affine manifolds with nilpotent holonomy. Comment. Math. Helvetica 56 (1981), 487–523.CrossRefGoogle Scholar
[5]Milnor, J.. On fundamental groups of complete affinely flat manifolds. Adv. in Math. 25 (1977), 178–187.CrossRefGoogle Scholar
[6]Perea, A. M.. Flat left-invariant connections adapted to the automorphism structure of a Lie group. Journal of Differential Geometry 16 (1981), 445–474.Google Scholar
[7]Moore, J. W. and Milnor, J. C.. On the struoture of Hopf algebras. Ann. of Maths. (2) 81 (1965), 211–264.Google Scholar
[8]Scheuneman, . Affine structures on three-step nilpotent Lie algebras. Proc. Amer. Math. Soc. 46 (1974), 451–454.CrossRefGoogle Scholar
[9]Segal, D.. Free left-symmetric algebras and an analogue of the Poincaré–Birkhoff–Witt theorem. Journal of Algebra 164 (1994), 750–772.CrossRefGoogle Scholar