Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie properties in associative algebras   Let K be a field, then we exhibit two matrices in the full nxn matrix algebra
M_{n}(K) which generate M_{n}(K) as a Lie K-algebra with the commutator Lie
product. We also study Lie centralizers of a not necessarily commutative
unitary algebra and obtain results which we hope will eventually be a step in
the direction of, firstly, proving that a Lie-nilpotent K-subspace (or a sub
Lie K-algebra) of a finite-dimensional associative algebra over K of index k
(say) generates a Lie-nilpotent associative subalgebra of much higher
nilpotency index, and secondly, in the light of the sharp upper bound for the
maximum (K-)dimension of a Lie-nilpotent K-subalgebra of M_{n}(K) of index k
(obtained earlier), finding an upper bound for the maximum dimension of a
Lie-nilpotent (of index k) sub Lie K-algebra of M_{n}(K). Finally, the
constructive elementary proof of the Skolem-Noether theorem for the matrix
algebra M_{n}(K) (appeared in the American Math. Monthly), in conjunction with
the well-known characteization of Lie automorphisms of M_{n}(K) (if the
characteristic of K is different from 2 and 3) in terms of, amongst others,
automorphisms and anti-automorhisms of M_{n}(K), leads us to a unifying
approach to constructively describe automorphisms and anti-automorphisms of
M_{n}(K).

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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg