Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gelfand-Kirillov dimension and Jordan algebras   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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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn