Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cocycle deformations for liftings of quantum linear spaces   Let $A$ be a Hopf algebra over a field $K$ of characteristic 0 and suppose
there is a coalgebra projection $\pi$ from $A$ to a sub-Hopf algebra $H$ that
splits the inclusion. If the projection is $H$-bilinear, then $A$ is isomorphic
to a biproduct $R #_{\xi}H$ where $(R,\xi)$ is called a pre-bialgebra with
cocycle in the category $_{H}^{H}\mathcal{YD}$. The cocycle $\xi$ maps $R
\otimes R$ to $H$. Examples of this situation include the liftings of pointed
Hopf algebras with abelian group of points $\Gamma$ as classified by
Andruskiewitsch and Schneider [AS1]. One asks when such an $A$ can be twisted
by a cocycle $\gamma:A\otimes A\rightarrow K$ to obtain a Radford biproduct. By
results of Masuoka [Ma1, Ma2], and Gr\"{u}nenfelder and Mastnak [GM], this can
always be done for the pointed liftings mentioned above.
  In a previous paper [ABM1], we showed that a natural candidate for a twisting
cocycle is {$\lambda \circ \xi$} where $\lambda\in H^{\ast}$ is a total
integral for $H$ and $\xi$ is as above. We also computed the twisting cocycle
explicitly for liftings of a quantum linear plane and found some examples where
the twisting cocycle we computed was different from {$\lambda \circ \xi$}. In
this note we show that in many cases this cocycle is exactly $\lambda\circ\xi$
and give some further examples where this is not the case. As well we extend
the cocycle computation to quantum linear spaces; there is no restriction on
the dimension.

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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
16
The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con