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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Lie algebras with nonintegral $q$-dimensions
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by V. M. Petrogradsky PDF
Proc. Amer. Math. Soc. 125 (1997), 649-656 Request permission


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:,
  • Received by editor(s): July 13, 1995
  • Additional Notes: The author was partially supported by ISF grant M22000(1994).
  • Communicated by: Ken Goodearl
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 649-656
  • MSC (1991): Primary 16P90, 17B30; Secondary 17B35
  • DOI:
  • MathSciNet review: 1363180