This paper is to study vertex operator superalgebras which are strongly generated by their weight-2 and weight-32 homogeneous subspaces. Among the main results, it proved that if such a superalgebra V simple, then V(2) has canonical commutative associative algebra structure equipped with non-degenerate symmetric bilinear form V(32) naturally V(2)-module V(2)-valued (C-valued) form, satisfying s...

Dirichlet branes are objects whose transverse coordinates in space are matrix– valued functions. This leads to considering a matrix algebra or, more generally, a Lie algebra, as the classical phase space of a certain dynamics where the multiplication of coordinates, being given by matrix multiplication, is nonabelian. Further quantising this dynamics by means of a ⋆–product introduces noncommut...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

X iv :m at h/ 05 12 40 7v 2 [ m at h. FA ] 1 8 Ja n 20 06 Notes on Matrix Valued Paraproducts Tao MEI 1 Abstract Denote by Mn the algebra of n×n matrices. We consider the dyadic paraproducts πb associated with Mn valued functions b, and show that the L(Mn) norm of b does not dominate ||πb||L2(l2n)→L2(l2n) uniformly over n. We also consider paraproducts associated with noncommutative martingales...