Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some classes of Z-graded Lie algebras   We study finite dimensional almost and quasi-effective prolongations of
nilpotent Z-graded Lie algebras, especially focusing on those having a
decomposable reductive structural subalgebra. Our assumptions generalize
effectiveness and algebraicity and are appropriate to obtain Levi-Mal\v{c}ev
and Levi-Chevalley decompositions and precisions on the heigth and other
properties of the prolongations in a very natural way. In a last section we
systematically present examples in which simple Lie algebras are obtained as
prolongations, for reductive structural algebras of type A, B, C and D, of
nilpotent Z-graded Lie algebras arising as their linear representations.

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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph