Abstract.
In this work we extend to superalgebras a result of Skosyrskii [Algebra and Logic, 18 (1) (1979) 49–57, Lemma 2] relating associative and Jordan structures. As an application, we show that the Gelfand-Kirillov dimension of an associative superalgebra coincides with that of its symmetrization, and that local finiteness is equivalent in associative superalgebras and in their symmetrizations. In this situation we obtain that having zero Gelfand-Kirillov dimension is equivalent to being locally finite.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Partially supported by MCYT and Fondos FEDER BFM2001-1938-C02-02, and MEC and Fondos FEDER MTM2004-06580-C02-01.
Partially supported by a F.P.I. Grant (Ministerio de Ciencia y Tecnología).
Rights and permissions
About this article
Cite this article
García, E. Gelfand-Kirillov Dimension and Local Finiteness of Symmetrizations of Associative Superalgebras. Mh Math 145, 229–238 (2005). https://doi.org/10.1007/s00605-005-0314-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-005-0314-3