Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Drinfel'd Double versus the Heisenberg Double for Hom-Hopf Algebras   Let $(A,\alpha)$ be a finite-dimensional Hom-Hopf algebra. In this paper we
mainly construct the Drinfel'd double $D(A)=(A^{op}\bowtie
A^{\ast},\alpha\otimes(\alpha^{-1})^{\ast})$ in the setting of Hom-Hopf
algebras by two ways, one of which generalizes Majid's bicrossproduct for Hopf
algebras (see \cite{M2}) and another one is to introduce the notion of dual
pairs of of Hom-Hopf algebras. Then we study the relation between the Drinfel'd
double $D(A)$ and Heisenberg double $H(A)=A\# A^{*}$, generalizing the main
result in \cite{Lu}. Especially, the examples given in the paper are not
obtained from the usual Hopf algebras.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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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: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin