Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal enveloping algebras and Poincar\'e-Birkhoff-Witt theorem for
  involutive Hom-Lie algebras   A Hom-type algebra is called involutive if its Hom map is multiplicative and
involutive. In this paper, we obtain an explicit construction of the free
involutive Hom-associative algebra on a Hom-module. We then apply this
construction to obtain the universal enveloping algebra of an involutive
Hom-Lie algebra. Finally we obtain a Poincar\'e-Birkhoff-Witt theorem for the
enveloping associative algebra of an involutive Hom-Lie algebra.

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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat