Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplier Hopf algebras imbedded in C$^*$-algebraic quantum groups   Let $(A,\Delta)$ be a locally compact quantum group and $(A_0,\Delta_0)$ a
regular multiplier Hopf algebra. We show that if $(A_0,\Delta_0)$ can in some
sense be imbedded in $(A,\Delta)$, then $A_0$ will inherit some of the analytic
structure of $A$. Under certain conditions on the imbedding, we will be able to
conclude that $(A_0,\Delta_0)$ is actually an algebraic quantum group with a
full analytic structure. The techniques used to show this, can be applied to
obtain the analytic structure of a $^*$-algebraic quantum group {\it in a
purely algebraic fashion}. Moreover, the {\it reason} that this analytic
structure exists at all, is that the one-parameter groups, such as the modular
group and the scaling group, are diagonizable. In particular, we will show that
necessarily the scaling constant $\mu$ of a $^*$-algebraic quantum group equals
1. This solves an open problem.

6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph