The Konov nesting of enveloping algebra into the ring with divisions

Authors

  • В. A. F. Wehrfritz School Math. Sci. and Westfield College, England

Keywords:

-

Abstract

In 1961 Р. М. Cohn proved that the universal enveloping algebra of any Lie algebra over a field-can be embedded into a division ring. (The Lie algebra is not assumed to be finite dimensional.) Cohn’s method is less than direct. We give a more explicit construction. These division rings have recently found uses in the theory of skew linear groups.

References

Cohn P. M. On the embedding of rings in skew fields// Proc. London Math. Soc.—1961.— 11, N 3.—P. 511—530.

Lichiman A. I. The residual nilpotence of the multiplicative group of a skew field generated by universal enveloping algebras//J. Algebra.— 1988.— 112.— P. 250—263.

Lichiman А. І. РІ-subrings and algebraic elements in enveloping algebras and their fields of fractions// Ibid.— 1989.— 121.— P. 139—154.

Lichtman A. I., Wehrfritz B. A. F. Finite-dimensional subalgebras in matrix rings over transcendental division algebras // Proc. Amer. Math. Soc.— 1989.— 106.— P. 335—344.

Jacobson N. Lie Algebras.— New York etc.: Interscience Pub., 1965.

Downloads

Published

07.07.1992

Issue

Section

Research articles

How to Cite

Wehrfritz В. A. F. “The Konov Nesting of Enveloping Algebra into the Ring With Divisions”. Ukrains’kyi Matematychnyi Zhurnal, vol. 44, no. 6, July 1992, pp. 729-35, https://umj.imath.kiev.ua/index.php/umj/article/view/8003.