Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Conjecture of Nowicki on Weitzenboeck derivations of polynomial
  algebras   The Weitzenboeck theorem states that the algebra of constants of a linear
locally nilpotent derivation of the polynomial algebra K[Z]=K[z_1,...,z_m] in m
variables over a field K of characteristic 0 is finitely generated. If m=2n and
the Jordan normal form of the derivation consists of Jordan cells of size 2
only, we may assume that K[Z]=K[X,Y] and the derivation sends y_i to x_i and
x_i to 0, i=1,...,n. Nowicki conjectured that the algebra of constants of this
derivation is generated by x_1,...,x_n and x_iy_j-x_jy_i, i<j. Recently this
conjecture was confirmed in the Ph.D. thesis of Khoury, and also by Derksen. In
this paper we give an elementary proof of the conjecture of Nowicki. Then we
find a very simple system of defining relations of the algebra of constants
which corresponds to the reduced Groebner basis of the related ideal with
respect to a suitable admissible order, and present an explicit basis of the
algebra of constants as a vector space.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas