The Konov nesting of enveloping algebra into the ring with divisions

Authors

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

Keywords:

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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.

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Published

07.07.1992

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Section

Research articles