caa a22 4500 606160604 CHVBK 20210128100630.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10468-014-9483-x doi (NATIONALLICENCE)springer-10.1007/s10468-014-9483-x Elliptic Algebra U q , p ( 𝖌 ̂ ) $U_{q,p}(\widehat {\mathfrak {g}})$ and Quantum Z -algebras [Elektronische Daten] [Rasha Farghly, Hitoshi Konno, Kazuyuki Oshima] A new definition of the elliptic algebra U q , p ( 𝔤 ̂ ) $U_{q,p}(\widehat {\mathfrak {g}})$ associated with an untwisted affine Lie algebra 𝔤 ̂ $\widehat {\mathfrak {g}}$ is given as a topological algebra over the ring of formal power series in p. We also introduce a quantum dynamical analogue of Lepowsky-Wilson's Z-algebras. The Z-algebra governs the irreducibility of the infinite dimensional U q , p ( 𝔤 ̂ ) $U_{q,p}({\widehat {\mathfrak {g}}})$ -modules. Some level-1 examples indicate a direct connection of the irreducible U q , p ( 𝔤 ̂ ) $U_{q,p}(\widehat {\mathfrak {g}})$ -modules to those of the W-algebras associated with the coset 𝔤 ̂ ⊕ 𝔤 ̂ ⊃ ( 𝔤 ̂ ) diag $\widehat {\mathfrak {g}}\oplus \widehat {\mathfrak {g}}\supset (\widehat {\mathfrak {g}})_{{diag}}$ with level (r − g − 1, 1) (g:the dual Coxeter number), which includes Fateev-Lukyanov's W B l -algebra. Springer Science+Business Media Dordrecht, 2014 Quantum group nationallicence Affine Lie algebra nationallicence Virasoro algebra nationallicence W-algebra nationallicence Z-algebra nationallicence Farghly Rasha Department of Mathematics, Graduate School of Science, Hiroshima University, 739-8521, Higashi-Hiroshima, Japan aut Konno Hitoshi Department of Mathematics, Tokyo University of Marine Science and Technology, 2-1-6 Etchyujima, 135-8533, Koto, Tokyo, Japan aut Oshima Kazuyuki Department of Mathematics, Center for General Education, Aichi Institute of Technology, 470-0392, Yakusa-cho, Toyota, Japan aut Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 103-135 1386-923X 18:1<103 2015 18 10468 https://doi.org/10.1007/s10468-014-9483-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9483-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farghly Rasha Department of Mathematics, Graduate School of Science, Hiroshima University, 739-8521, Higashi-Hiroshima, Japan aut NATIONALLICENCE 700 1- Konno Hitoshi Department of Mathematics, Tokyo University of Marine Science and Technology, 2-1-6 Etchyujima, 135-8533, Koto, Tokyo, Japan aut NATIONALLICENCE 700 1- Oshima Kazuyuki Department of Mathematics, Center for General Education, Aichi Institute of Technology, 470-0392, Yakusa-cho, Toyota, Japan aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 103-135 1386-923X 18:1<103 2015 18 10468