Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Poincar\'e-Birkhoff-Witt theorem for generalized color Lie algebras   A proof of Poincar\'e-Birkhoff-Witt theorem is given for a class of
generalized Lie algebras closely related to the Gurevich S-Lie algebras. As
concrete examples, we construct the positive (negative) parts of the quantized
universal enveloping algebras of type A_n and M_{p,q,e}(n,K), which is a
non-standard quantum deformation of GL(n). In particular, we get, for both
algebras, a unified proof of the Poincar\'e-Birkhoff-Witt theorem and we show
that they are genuine universal enveloping algebras of certain generalized Lie
algebras.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: stat