Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices   In this paper we propose versions of the associative Yang-Baxter equation and
higher order $R$-matrix identities which can be applied to quantum dynamical
$R$-matrices. As is known quantum non-dynamical $R$-matrices of Baxter-Belavin
type satisfy this equation. Together with unitarity condition and skew-symmetry
it provides the quantum Yang-Baxter equation and a set of identities useful for
different applications in integrable systems. The dynamical $R$-matrices
satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation
between the dynamical and non-dynamical cases is described by the IRF-Vertex
transformation. An alternative approach to quantum (semi-)dynamical
$R$-matrices and related quantum algebras was suggested by Arutyunov, Chekhov
and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The
purpose of this paper is twofold. First, we prove that the ACF elliptic
$R$-matrix satisfies the associative Yang-Baxter equation with shifted spectral
parameters. Second, we directly prove a simple relation of the IRF-Vertex type
between the Baxter-Belavin and the ACF elliptic $R$-matrices predicted
previously by Avan and Rollet. It provides the higher order $R$-matrix
identities and an explanation of the obtained equations through those for
non-dynamical $R$-matrices. As a by-product we also get an interpretation of
the intertwining transformation as matrix extension of scalar theta function
likewise $R$-matrix is interpreted as matrix extension of the Kronecker
function. Relations to the Gervais-Neveu-Felder equation and identities for the
Felder's elliptic $R$-matrix are also discussed.

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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph