A classification of regressive transformation semigroups on chains

For each subchain X?? of a chain X, let T _RE (X,X??) denote the semigroup under composition of all full regressive transformations, ??:X??X?? satisfying x????x for all x??X. Necessary and sufficient conditions for T _RE (X,X??) and T _RE (Y,Y??) to be isomorphic are given. This isomorphism theorem is applied to classify the semigroup of regressive transformations T _RE (X,X??) where X is one of several familiar subchains of ?, the chain of real numbers.     

C 2-Cofiniteness of the Vertex Algebra When L is a Nondegenerate Even Lattice

We study the Lie nilpotency and Lie n-Engel properties of symmetric elements under oriented involutions. In some cases, the results obtained are similar to the ones in the case of the classical involution, but interesting new situations arise.     

Splitting criteria for homotopy functors of spectra

We explore the interaction between the Taylor tower and cotower, as defined in deriving calculus with cotriples and dual calculus for functors to spectra of functors of spectra. This leads to new splitting criteria which generalize the results in dual calculus for functors to spectra.