Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groebner-Shirshov basis of the universal enveloping Rota-Baxter algebra
  of a Lie algebra   Consider the class RBLie of Lie algebras equipped with a Rota---Baxter
operator. Then the forgetful functor RBLie --> Lie has a left adjoint one
denoted by $U_{RB}(\cdot)$. We prove an "operator" analogue of the
Poincare---Birkhoff---Witt theorem for $U_{RB}(L)$, where $L$ is an arbitrary
Lie algebra, by means of Gr\"obner---Shirshov bases theory for Lie algebras
with an additional operator.

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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph