Geodesic
On Abelianity Lines in Elliptic $W$-Algebras
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $\mathcal{A}_{q,p}\big(\widehat{\mathfrak{gl}}(N)_{c}\big)$. We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space ($p, q, c$). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson brackets structures are then computed for which some universal features are described.
Keywords: elliptic quantum algebras, $W$-algebras. 
@article{SIGMA_2020_16_a93,
     author = {Jean Avan and Luc Frappat and Eric Ragoucy},
     title = {On {Abelianity} {Lines} in {Elliptic} $W${-Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a93/}
}
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Jean Avan; Luc Frappat; Eric Ragoucy. On Abelianity Lines in Elliptic $W$-Algebras. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a93/

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