Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generators and defining relations for ring of invariants of commuting
  locally nilpotent derivations or automorphisms   Let $A$ be an algebra over a field $K$ of characteristic zero, let $\d_1,
>..., \d_s\in \Der_K(A)$ be {\em commuting locally nilpotent}
  $K$-derivations such that $\d_i(x_j)=\d_{ij}$, the Kronecker delta, for some
elements $x_1,..., x_s\in A$. A set of algebra generators for the algebra
$A^\d:= \cap_{i=1}^s\ker (\d_i)$ is found {\em explicitly} and a set of {\em
defining relations} for the algebra $A^\d$ is described. Similarly, given a set
$\s_1, ..., \s_s\in \Aut_K(A)$ of {\em commuting}
  $K$-automorphisms of the algebra $A$ such that the maps $\s_i-{\rm id_A}$ are
{\em locally nilpotent} and $\s_i (x_j)=x_j+\d_{ij}$, for some elements
$x_1,..., x_s\in A$. A set of algebra generators for the algebra $A^\s:=\{a\in
A | \s_1(a)=... =\s_s(a)=a\}$ is found {\em explicitly} and a set of defining
relations for the algebra $A^\s$ is described. In general, even for a {\em
finitely generated noncommutative} algebra $A$ the algebras of invariants $A^\d
$ and $A^\s $ are {\em not} finitely generated, {\em not} (left or right)
Noetherian and {\em does not} satisfy finitely many defining relations (see
examples). Though, for a {\em finitely generated commutative} algebra $A$ {\em
always} the {\em opposite} is true. The derivations (or automorphisms) just
described appear often in may different situations after (possibly) a
localization of the algebra $A$.

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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ