In this paper the problem of compatibility between a nonlinear connection and other geometric structures on Lie algebroids is studied. The notion of dynamical covariant derivative is introduced and a metric nonlinear connection is found in the more general case of Lie algebroids. We prove that the canonical nonlinear connection induced by a regular Lagrangian on a Lie algebroid is the unique co...

Abstract. The Virasoro–Zamolodchikov Lie algebra w∞ has been widely studied in string theory and in conformal field theory, motivated by the attempts of developing a satisfactory theory of quantization of gravity. The renormalized higher powers of quantum white noise (RHPWN) ∗-Lie algebra has been recently investigated in quantum probability, motivated by the attempts to develop a nonlinear gen...

Starting from the well-known quantum Miura transformation for the Lie algebra An, we compute explicitly the OPEs for n = 3 and 4. The primary fields with spin 3, 4 and 5 are found (for general n). By using these primary fields and the OPEs from quantum Miura transformation, we derive the complete structure of the nonlinear W4 and W5 algebras. It is known that the quantum Miura transformation fo...