Free field approach to solutions of the quantum Knizhnik-Zamolodchikov equations.
Free field construction of D-branes in rational models of CFT and Gepner models.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
From Poisson algebras to Gerstenhaber algebras
Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...
Functions on the universal cover of the prinicpal nilpotent orbit.
Fundamental representations of Yangians and singularities of R-matrices.
Fusion algebras for superconformal field theories through coinvariants. II: super-Virasoro-symmetry.