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

 

On Lie algebras with nonintegral $q$-dimensions


Author: V. M. Petrogradsky
Journal: Proc. Amer. Math. Soc. 125 (1997), 649-656
MSC (1991): Primary 16P90, 17B30; Secondary 17B35
MathSciNet review: 1363180
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Abstract: In a recent paper an author has suggested a series of dimensions which include as first terms dimension of a vector space, Gelfand-Kirillov dimenision and superdimension. In terms of these dimensions the growth of free polynilpotent finitely generated Lie algebras has been specified. All these dimensions are integers. In this paper we study for all levels $q=2,3\dots $ what numbers $\alpha >0$ can be a $q$-dimension of some Lie (associative) algebra.


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Additional Information

V. M. Petrogradsky
Affiliation: Department of Mathematics, Branch of Moscow State University in Ulyanovsk, 432700 Lev Tolstoy 42, Ulyanovsk, Russia
Address at time of publication: Department of Mathematics, University of Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
Email: vmp@mmf.univ.simbirsk.su, petrogra@Mathematik.Uni-Bielefeld.de

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03679-4
PII: S 0002-9939(97)03679-4
Received by editor(s): July 13, 1995
Additional Notes: The author was partially supported by ISF grant M22000(1994).
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society