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HNN-extensions of lie algebras |
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| Authors: | A. I. Lichtman M. Shirvani |
| Affiliation: | Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada quad T6G 2G1 ; Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada quad T6G 2G1 |
| Abstract: | We define HNN-extensions of Lie algebras and study their properties. In particular, a sufficient condition for freeness of subalgebras is obtained. We also study differential HNN-extensions of associative rings. These constructions are used to give short proofs of Malcev's and Shirshov's theorems that an associative or Lie algebra of finite or countable dimension is embeddable into a two-generator algebra. |
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