We construct operators t ( z ) in the elliptic algebra A q,p ( sl (2) c ) closing an exchange algebra when p m = q c +2 for m ∈ Z . In addition they commute when p = q 2 k for k non-zero integer, and they belong to the center of A q,p ( sl (2) c ) when k is odd. The Poisson structures obtained for t ( z ) in these classical limits are identical to the q -deformed Virasoro Poisson algebra, characterizing the structures at p ≠ q 2 k as new W q,p ( sl (2)) algebras.
New ${cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${cal A}_{q,p}(widehat {sl}(2)_c)$
ROSSI, Marco;
1998-01-01
Abstract
We construct operators t ( z ) in the elliptic algebra A q,p ( sl (2) c ) closing an exchange algebra when p m = q c +2 for m ∈ Z . In addition they commute when p = q 2 k for k non-zero integer, and they belong to the center of A q,p ( sl (2) c ) when k is odd. The Poisson structures obtained for t ( z ) in these classical limits are identical to the q -deformed Virasoro Poisson algebra, characterizing the structures at p ≠ q 2 k as new W q,p ( sl (2)) algebras.File in questo prodotto:
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