Rashkova, Tsetska Gr. Gelfand-Kirillov dimension for non-associative algebras. (English) Zbl 1013.17500 Bull. Greek Math. Soc. 35, 31-39 (1993). An analogue of the Gelfand-Kirillov dimension for nonassociative algebras is defined as follows: \[ \text{GK-}\dim A=\limsup_{n\to \infty} \log_n d_V(n), \] where \(A\) denotes a not necessarily associative \(k\)-algebra, \(\text{char }k=0\), \(V_n\) the \(k\)-subspace of \(A\) spanned by all monomials in the finite generality subset \(V\) (of \(A\)) of length \(\leq n\) and \(d_V(n)=\dim_k V_n\).The author shows that for a Lie algebra \(L\) GK-\(\dim L\) can take any natural number, that no Lie algebra can have GK-\(\dim L\) strictly between 0 and 1, and GK-\(\dim L =0\) in case \(L\) is a finitely generated nilpotent Lie algebra. Reviewer: O.Ninnemann (Berlin) MSC: 17A99 General nonassociative rings 16P90 Growth rate, Gelfand-Kirillov dimension 17B30 Solvable, nilpotent (super)algebras Keywords:Gelfand-Kirillov dimension; nonassociative algebras PDFBibTeX XMLCite \textit{T. Gr. Rashkova}, Bull. Greek Math. Soc. 35, 31--39 (1993; Zbl 1013.17500) Full Text: EuDML