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arXiv · 1508.04707

Gelfand-Kirillov dimension and Jordan algebras

Centrone Lucio·Martino Fabrizio
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Abstract

Let A be any associative algebra graded by a finite abelian group G, then if we denote by GKdim_k(A) and GKdim^G_k (A) the Gelfand-Kirillov dimension of its relatively free algebra and its relatively free G-graded algebra in k variables respectively, then GKdim_k(A)\leq GKdim^G_k (A). We show a counterexample of the previous result for Jordan algebras (hence non-associative). In particular, there exists a $Z_2$-grading on $UJ_n$, the Jordan algebra of $n\times n$ upper triangular matrices, n equal to 2 or 3, such that the previous inequality does not hold.

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Centrone Lucio, Martino Fabrizio. 2016-10-07. Gelfand-Kirillov dimension and Jordan algebras. https://arxiv.org/abs/1508.04707

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