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A connected Lie group G is generated by its two 1-parametric subgroups exp(tX), exp(tY ) if and only if the Lie algebra of G is generated by {X, Y }. We consider decompositions of elements of G into a product of such exponentials with times t > 0 and study the problem of minimizing the total time of the decompositions for a fixed element of G. We solve this(More)
In this paper, we generalize a result by Berman and Billig on weight modules over Lie algebras with polynomial multiplication. More precisely, we show that a highest weight module with an exp-polynomial “highest weight” has finite dimensional weight spaces. We also get a class of irreducible weight modules with finite dimensional weight spaces over(More)
We construct vertex operator representations for the full (N + 1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine slN VOA and a twisted Heisenberg-Virasoro VOA. The modules for the toroidal VOA are also modules for the toroidal Lie(More)
Magnetic hydrodynamics with asymmetric stress tensor. In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial 2-cocycle. We use the Lie algebra approach to prove the energy(More)
Toroidal Lie algebras are very natural multi-variable generalizations of affine Kac-Moody algebras. The theory of affine Lie algebras is rich and beautiful, having connections with diverse areas of mathematics and physics. Toroidal Lie algebras are also proving themselves to be useful for the applications. Frenkel, Jing and Wang [FJW] used representations(More)
We show that the representation theory for the toroidal extended affine Lie algebra is controlled by a VOA which is a tensor product of four VOAs: a sub-VOA V + Hyp of a hyperbolic lattice VOA, affine ̂̇g and ŝlN VOAs and a Virasoro VOA. A tensor product of irreducible modules for these VOAs admits the structure of an irreducible module for the toroidal(More)