Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally compact quantum groups in the von Neumann algebraic setting   In this paper we complete in several aspects the picture of locally compact
quantum groups. First of all we give a definition of a locally compact quantum
group in the von Neumann algebraic setting and show how to deduce from it a
C*-algebraic quantum group. Further we prove several results about locally
compact quantum groups which are important for applications, but were not yet
settled in our paper "Locally compact quantum groups". We prove a serious
strengthening of the left invariance of the Haar weight, and we give several
formulas connecting the locally compact quantum group with its dual. Loosely
speaking we show how the antipode of the locally compact quantum group
determines the modular group and modular conjugation of the dual locally
compact quantum group.

14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat