Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Multiparametric Quantum Superspace and Its Logarithmic Extension   We introduce a multiparametric quantum superspace with $m$ even generators
and $n$ odd generators whose commutation relations are in the sense of Manin
such that the corresponding algebra has a Hopf superalgebra. By using its Hopf
superalgebra structure, we give a bicovariant differential calculus and some
related structures such as Maurer-Cartan forms and the correspoinding vector
fields. It is also shown that there exists a quantum supergroup related with
these vector fields. Morever, we introduce the logarithmic extension of this
quantum superspace in the sense that we extend this space by the series
expansion of the logarithm of the grouplike generator, and we define new
elements with nonhomogeneous commutation relations. It is clearly seen that
this logarithmic extension is a generalization of the $\kappa-$Minkowski
superspace. We give the bicovariant differential calculus and the related
algebraic structures on this extension. All noncommutative results are found to
reduce to those of the standard superalgebra when the deformation parameters of
the quantum (m+n)-superspace are set to one.

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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th