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- W2059527011 abstract "We investigate properties of the sl(n) automorphic elliptic algebra documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n))$end{document}E(sl(n)). We prove it to be documentclass[12pt]{minimal}begin{document}$mathbb {Z}$end{document}Z quasi-graded Lie algebra which could be viewed as a deformation of a graded loop algebra. We show that it admits the decomposition into the direct sum of two subalgebras: documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n))= mathfrak {E}(sl(n))_+ + mathfrak {E}(sl(n))_-$end{document}E(sl(n))=E(sl(n))++E(sl(n))− consistent with the described quasi-grading. We prove that documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n))^*_{pm }=mathfrak {E}(sl(n))_{mp }$end{document}E(sl(n))±*=E(sl(n))∓, i.e., Lie algebras documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n)),$end{document}E(sl(n)), documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n))_+ ,$end{document}E(sl(n))+, and documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n))_-$end{document}E(sl(n))− constitute the Manin triple. We explicitly construct a central extension of documentclass[12pt]{minimal}begin{document}$mathfrak {E}(sl(n))$end{document}E(sl(n)). We find its algebra of differentiations and its central extension which coincide with the quasi-graded deformation of the Virasoro algebra." @default.
- W2059527011 created "2016-06-24" @default.
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- W2059527011 date "2012-02-01" @default.
- W2059527011 modified "2023-09-23" @default.
- W2059527011 title "Quasi-periodic functions on the torus and <i>sl</i>(<i>n</i>)-elliptic Lie algebra" @default.
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- W2059527011 doi "https://doi.org/10.1063/1.3681211" @default.
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