Their topics include quantum polynomials, isomorphisms and derivations of algebras, semigroup properties of cooperations on finite sets, continuous co-algebra endomorphisms of some complete ultra-metric Hopf algebras, irreducible sub-algebras of matrix Weyl algebras, the length of conjugacy classes and P-nilpotence of finite groups, a symbolic calculus on defect revisions of axiomatic systems, and conformal field theory and modular functor.

If V is a simple Euclidean Jordan algebra of rank r and dimension n, then the following isomorphisms [equivalent] hold.

Furthermore, in the case of Riesz bases we prove that those functions are isomorphisms.