Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-Linear Algebras and Integrability (the Heisenberg Picture)   We study Poisson and operator algebras with the ''quasi-linear property''
from the Heisenberg picture point of view. This means that there exists a set
of one-parameter groups yielding an explicit expression of dynamical variables
(operators) as functions of ''time'' $t$. We show that many algebras with
nonlinear commutation relations such as the Askey-Wilson, $q$-Dolan-Grady and
others satisfy this property. This provides one more (explicit Heisenberg
evolution) interpretation of the corresponding integrable systems.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
9
The categories of this paper are: nlin
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat