Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and
  Rota-Baxter Lie bialgebras   In this paper, first we introduce the notion of quadratic Rota-Baxter Lie
algebras of arbitrary weight, and show that there is a one-to-one
correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter
Lie algebras of nonzero weight. Then we introduce the notions of matched pairs,
bialgebras and Manin triples of Rota-Baxter Lie algebras of arbitrary weight,
and show that Rota-Baxter Lie bialgebras, Manin triples of Rota-Baxter Lie
algebras and certain matched pairs of Rota-Baxter Lie algebras are equivalent.
The coadjoint representations and quadratic Rota-Baxter Lie algebras play
important roles in the whole study. Finally we generalize some results to the
Lie group context. In particular, we show that there is a one-to-one
correspondence between factorizable Poisson Lie groups and quadratic
Rota-Baxter Lie groups.

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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom