Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on Radford's $S^4$ formula   In this note, we show that Radford's formula for the fourth power of the
antipode can be proven for any regular multiplier Hopf algebra with integrals
(algebraic quantum groups). This of course not only includes the case of a
finite-dimensional Hopf algebra but also the case of any
  Hopf algebra with integrals (co-Frobenius Hopf algebras). The proof follows
in a few lines from well-known formulas in the theory of regular multiplier
Hopf algebras with integrals.
  We discuss these formulas and their importance in this theory. We also
mention their generalizations to the (in a certain sense) more general theory
of locally compact quantum groups. Doing so, and also because the proof of the
main result itself is very short, the present note becomes largely of an
expository nature.

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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: chem-ph