Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constituents of graded Lie algebras of maximal class and chain lengths
  of thin Lie algebras   Thin Lie algebras are infinite-dimensional graded Lie algebras
$L=\bigoplus_{i=1}^{\infty}$, with $\dim(L_1)=2$ and satisfying a covering
property: for each $i$, each nonzero $z\in L_i$ satisfies $[zL_1]=L_{i+1}$. It
follows that each homogeneous components $L_i$ is either one- or
two-dimensional, and in the latter case is called a diamond. Hence $L_1$ is a
diamond, and if there are no other diamonds then $L$ is a graded Lie algebra of
maximal class.
  We present simpler proofs of some fundamental facts on graded Lie algebras of
maximal class, and on thin Lie algebras, based on a uniform method, with
emphasis on a polynomial interpretation. Among else, we determine the possible
values for the most fundamental parameter of such algebras, which is the
dimension of their largest metabelian quotient.

29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph