Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central invariants and enveloping algebras of braided Hom-Lie algebras   Let $(H,\alpha)$ be a monoidal Hom-Hopf algebra and $^{H}_{H}\mathcal{HYD}$
the Hom-Yetter-Drinfeld category over $(H,\alpha)$. Then in this paper, we
first introduce the definition of braided Hom-Lie algebras and show that each
monoidal Hom-algebra in $^{H}_{H}\mathcal{HYD}$ gives rise to a braided Hom-Lie
algebra. Second, we prove that if $(A,\beta)$ is a sum of two $H$-commutative
monoidal Hom-subalgebras, then the commutator Hom-ideal $[A,A]$ of $A$ is
nilpotent. Also, we study the central invariant of braided Hom-Lie algebras as
a generalization of generalized Lie algebras. Finally, we obtain a construction
of the enveloping algebras of braided Hom-Lie algebras and show that the
enveloping algebras are $H$-cocommutative Hom-Hopf algerbas.

28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph