Between gl{infinity} and sl{sub N} affine algebras. I. geometrical actions
- MIT, Moscow (Russian Federation)
We consider the central extended gl({infinity}) Lie algebra and a set of its subalgebras parametrized by {vert_bar}q{vert_bar} = 1, which coincides with the embedding of the quantum tori Lie algebras (QTLA) in gl({infinity}). For q{sup N} = 1 there exists an ideal, and a factor over this ideal is isomorphic to an al{sub N}(z) affine algebra. For a generic value q the corresponding subalgebras are dense in gl({infinity}). Thus, they interpolate between gl({infinity}) and sl{sub N}(z). AU these subalgebras are fixed points of automorphisms of gl({infinity}). Using the automorphisms, we construct geometrical actions for the subalgebras, starting from the Kirillov-Kostant form and the corresponding geometrical action for gl({infinity}).
- OSTI ID:
- 390976
- Journal Information:
- Theoretical and Mathematical Physics, Vol. 100, Issue 1; Other Information: PBD: Jan 1995; TN: Translated from Teoreticheskaya i Matematicheskaya Fizika; 100: No. 1, 82-96(Jul 1994)
- Country of Publication:
- United States
- Language:
- English
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