A Hilbert module over a planar algebra is essentially a Hilbert module over a eanonieally defined algebra spanned by the annular tangles in It follows that any planar algebra containing is a module over and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar...

Let ∈ ℂ be a nontrivial involution; i.e., = ≠ ±. We say that ∈ ℂ is -symmetric (-skew symmetric) if = ( = − ). Let be one of the following subsets of ℂ: (i) -symmetric matrices; (ii) Hermitian -symmetric matrices; (iii) -skew symmetric matrices; (iv) Hermitian -skew symmetric...

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for...

Let := () be defined over an algebraically closed field of prime characteristic . Put and let { = − , = } be a base of the root system Φ of . For a Weyl group element and for a character λ ∈ (), we put where = λ, mod and denotes a Borel subalgebra of generated by positive root vectors...

In this paper, we shall study the eigenvalue problem of a singular quasilinear elliptic equation. We will show that many results about the eigenvalues and eigenfunctions in the non-singular case can be extended to the more general singular case, e.g., the first eigenvalue λ is associated to a...

Let be any -type Lie algebra with ≥ 2 over an algebraically closed field of characteristic 5. Let be an irreducible -module corresponding to some points and let be its corresponding representation. In this paper, in order to prove that the equality about the versus problem out of the 7 Clay...