SEMI-REGULAR MASAS OF TRANSFINITE LENGTH

Semi-regular masas of transfinite length

In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite II1 factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each n ∈ N, finding masas for which this procedure terminates at the n-th stage. Such masas are said to have length n. In this paper we...

A note on semi-regular locales

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

Spectra of semi-regular polytopes

We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few different techniques are employed: the most sophisticated, which relates the 1-skeleton of the polytope to a Cayley graph, is based on methods akin to those of Lovász and Babai ([L], [B]). It turns out that the algebraic degree of the eigenvalues is at most 5, achieved at two 3-dimensional solids.

Transfinite Equations in Transfinite Strings

Strongly Regular Semi-Cayley Graphs

We consider strongly regular graphs r = (V, E) on an even number, say 2n, of vertices which admit an automorphism group G of order n which has two orbits on V. Such graphs will be called strongly regular semi-Cayley graphs. For instance, the Petersen graph, the Hoffman-Singleton graph, and the triangular graphs T(q) with q = 5 mod 8 provide examples which cannot be obtained as Cayley graphs. We...