ISSN:
1573-9333

Source:
Springer Online Journal Archives 1860-2000

Topics:
Mathematics
,
Physics

Notes:
Abstract We consider the central extended $$\widehat{gl}(\infty )$$ Lie algebra and a set of its subalgebras parametrized by |q|=1, which coincides with the embedding of the quantum tori Lie algebras (QTLA) in $$\widehat{gl}(\infty )$$ . Forq N=1 there exists an ideal, and a factor over this ideal is isomorphic to an $$\widehat{sl}_{N(z)} $$ affine algebra. For a generic valueq the corresponding subalgebras are dense in $$\widehat{gl}(\infty )$$ . Thus, they interpolate between $$\widehat{gl}(\infty )$$ and $$\widehat{sl}_{N(z)} $$ . All these subalgebras are fixed points of automorphism of $$\widehat{gl}(\infty )$$ . Using the automorphisms, we construct geometrical actions for the subalgebras, starting from the Kirillov-Kostant form and the corresponding geometrical action for $$\widehat{gl}(\infty )$$ .

Type of Medium:
Electronic Resource

Permalink