Each v ∈ V has a vertex operator Y (v, z) = ∑ n∈Z vnz −n−1 attached to it, where vn ∈ EndV. For the conformal vector ω we write Y (ω, z) = ∑ n∈Z L(n)z . If v is homogeneous of weight k, that is v ∈ Vk, then one knows that vn : Vm → Vm+k−n−1 and in particular the zero mode o(v) = vwtv−1 induces a linear operator on each Vm. We extend the “o” notation linearly to V, so that in general o(v) is the...

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

We discuss the notion of noncommutative point derivations for operator algebras. We look at the noncommutative point derivations for the quiver algebras, A(Cn) where Cn is the directed graph with n-vertices and n-edges forming a cycle. For the algebras Mn ⊗ A(D) and A(Cn) we classify when non-trivial point derivations can occur. We use the point derivations to show that every derivation on A(Cn...

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gammafunctions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral...

This paper describes a new spatial operator algebra for the dynamics of general{topology rigid multibody systems. Spatial operators allow a concise and systematic formulation of the dynamical equations of motion of multibody systems and the development of e cient computational algorithms. Equations of motion are developed for progressively more complex systems: serial chains, topological trees,...

We present some nonlinear characterizations of the automorphisms of the operator algebra B(H) and the function algebra C(X) by means of their spectrum preserving properties.

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

A recently developed spatial operator algebra for manipulator modeling, control and tra-jectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The eeect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be eeciently ob...

We establish a geometric condition that determines when a type III von Neumann algebra arises from a foliation whose holonomy becomes affine with respect to a suitable transverse coordinate system. Under such an assumption the Godbillon-Vey class of the foliation becomes trivial in contrast to the case considered in Connes’s famous theorem.