Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the order of the antipode of a pointed Hopf algebra   Let $k$ be a field and let $H$ denote a pointed Hopf $k$-algebra with
antipode $S$. We are interested in determining the order of $S$. Building on
the work done by Taft and Wilson $[7]$, we define an invariant for $H$, denoted
$m_{H}$, and prove that the value of this invariant is connected to the order
of $S$. In the case where $\operatorname{char}k=0$, it is shown that if $S$ has
finite order then it is either the identity or has order $2m_{H}$. If in
addition $H$ is assumed to be coradically graded, it is shown that the order of
$S$ is finite if and only if $m_{H}$ is finite. We also consider the case where
$\operatorname{char}k=p>0$, generalising the results of $[7]$ to the
infinite-dimensional setting.

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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: acc-phys