LIE-ADMISSIBLE ALGEBRAS AND THE VIRASORO ALGEBRA

Let A be an (nonassociative) algebra with multiplication xy over a field F, and denote by $A^-$ the algebra with multiplication [x, y] = xy - yx$ defined on the vector space A. If $A^-$ is a Lie algebra, then A is called Lie-admissible. Lie-admissible algebras arise in various topics, including geometry of invariant affine connections on Lie groups and classical and quantum mechanics(see [2, 5, 6, 7] and references therein).