Algorithmic construction of Chevalley bases

We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When applied to a simple Chevalley Lie algebra in characteristic p⩾5, our algorithm has complexity involving the seventh power of the Lie rank, which is likely to be close to best possible.

HAMILTONIAN FORMALISM OF TWO-LOOP WZNW MODEL

The Hamiltonian canonical formalism of two-dimensional WZNW model based on an arbitrary affine Lie algebra is given under the Chevalley basis. The Poisson brackets of conserved chiral currents are calculated, which turn out to be the classical two-loop Kac-Moody current algebras.