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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

HNN-extensions of lie algebras


Authors: A. I. Lichtman and M. Shirvani
Journal: Proc. Amer. Math. Soc. 125 (1997), 3501-3508
MSC (1991): Primary 17B05; Secondary 16S10, 17B01
MathSciNet review: 1423316
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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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Additional Information

A. I. Lichtman
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: lichtman@cs.uwp.edu

M. Shirvani
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: mazi@schur.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04124-5
PII: S 0002-9939(97)04124-5
Received by editor(s): March 22, 1996
Received by editor(s) in revised form: July 9, 1996
Additional Notes: The first author was partially supported by the NSF Grant No. 144-F1181, and the second author by NSERC, Canada.
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society