We investigate properties of the sl(n) automorphic elliptic algebra c{fraktur}(sl(n)). We prove it to be 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: c{fraktur}(sl(n)) = c{fraktur}(sl(n)) + + c{fraktur}(sl(n)) - consistent with the described quasi-grading. We prove that c{fraktur}(sl(n)) ± * = c{fraktur}(sl(n)) ±, i.e., Lie algebras c{fraktur}(sl(n)), c{fraktur}(sl(n)) + c{fraktur}(sl(n)) - and constitute the Manin triple. We explicitly construct a central extension of c{fraktur}(sl(n)). We find its algebra of differentiations and its central extension which coincide with the quasi-graded deformation of the Virasoro algebra. © 2012 American Institute of Physics.

Skrypnyk, T. (2012). Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra. JOURNAL OF MATHEMATICAL PHYSICS, 53(2), 023502 [10.1063/1.3681211].

Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra

SKRYPNYK, TARAS
Primo
2012

Abstract

We investigate properties of the sl(n) automorphic elliptic algebra c{fraktur}(sl(n)). We prove it to be 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: c{fraktur}(sl(n)) = c{fraktur}(sl(n)) + + c{fraktur}(sl(n)) - consistent with the described quasi-grading. We prove that c{fraktur}(sl(n)) ± * = c{fraktur}(sl(n)) ±, i.e., Lie algebras c{fraktur}(sl(n)), c{fraktur}(sl(n)) + c{fraktur}(sl(n)) - and constitute the Manin triple. We explicitly construct a central extension of c{fraktur}(sl(n)). We find its algebra of differentiations and its central extension which coincide with the quasi-graded deformation of the Virasoro algebra. © 2012 American Institute of Physics.
Articolo in rivista - Articolo scientifico
Statistical and Nonlinear Physics; Mathematical Physics
English
2012
53
2
023502
023502
none
Skrypnyk, T. (2012). Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra. JOURNAL OF MATHEMATICAL PHYSICS, 53(2), 023502 [10.1063/1.3681211].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/66790
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