Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nilpotency degree of the algebra with identity x^n=0   Denote by C_{n,d} the nilpotency degree of a relatively free algebra
generated by d elements and satisfying the identity x^n=0. Under assumption
that the characteristic p of the base field is greater than n/2, it is shown
that C_{n,d}<n^{log_2(3d+2)+1} and C_{n,d}<4 2^{n/2} d. In particular, it is
established that the nilpotency degree C_{n,d} has a polynomial growth in case
the number of generators d is fixed and p > n/2. For p\neq2 the nilpotency
degree C_{4,d} is described with deviation 4 for all d. As an application, a
finite generating set for the algebra R^{GL(n)} of GL(n)-invariants of d
matrices is established in terms of C_{n,d}. Several conjectures are
formulated.

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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con