Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Analogy of Poisson Geometry, Related Dendriform Algebras and
  Rota-Baxter Operators   We will introduce an associative (or quantum) version of Poisson structure
tensors. This object is defined as an operator satisfying a "generalized"
Rota-Baxter identity of weight zero. Such operators are called generalized
Rota-Baxter operators. We will show that generalized Rota-Baxter operators are
characterized by a cocycle condition so that Poisson structures are so. By
analogy with twisted Poisson structures, we propose a new operator "twisted
Rota-Baxter operators" which is a natural generalization of generalized
Rota-Baxter operators. It is known that classical Rota-Baxter operators are
closely related with dendriform algebras. We will show that twisted Rota-Baxter
operators induce NS-algebras which is a twisted version of dendriform algebra.
The twisted Poisson condition is considered as a Maurer-Cartan equation up to
homotopy. We will show the twisted Rota-Baxter condition also is so. And we
will study a Poisson-geometric reason, how the twisted Rota-Baxter condition
arises.

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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: chem-ph