We investigate properties of the sl ( n ) automorphic elliptic algebra E (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: E (sl(n))= E (sl(n)) + + E (sl(n)) - consistent with the described quasi-grading. We prove that E (sl(n)) ± * = E (sl(n)) ∓ , i.e., Lie algebras E (sl(n)), E (sl(n)) + , and E (sl(n)) - constitute the Manin triple. We explicitly construct a central extension of E (sl(n)) . We find its algebra of differentiations and its central extension which coincide with the quasi-graded deformation of the Virasoro algebra.
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Quasi-periodic functions on the torus and sl ( n )-elliptic Lie algebra
Skrypnyk, T.
Follow Journal of Mathematical Physics
, Volume 53 (2)
American Institute of Physics – Feb 1, 2012
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