Deformations of Coalgebra Morphisms

Coalgebra-to-Algebra Morphisms

Given a coalgebra p for HG, an algebra s for GH and the obvious notion of morphism from coalgebra to algebra, we observe that morphisms from Gp to s correspond to morphisms from p to Hs in the manner of an adjunction even when there is no adjunction between G and H. This appears to be one of the basic phenomena underlying the transport of special algebras. A proof of Freyd’s Iterated Square The...

Coalgebra Morphisms Subsume Open Maps

Superintegrable Deformations of the Smorodinsky–Winternitz Hamiltonian

A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky–Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the general connection between coalgebra symmetry and quasi-maximal superintegrability is analysed. The notion of comodule algebra symmetry is also shown to be app...

On descent for coalgebras and type transformations

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

Long range integrable oscillator chains from quantum algebras

Completely integrable Hamiltonians defining classical mechanical systems of N coupled oscillators are obtained from Poisson realizations of Heisenberg–Weyl, harmonic oscillator and sl(2, IR) coalgebras. Various completely integrable deformations of such systems are constructed by considering quantum deformations of these algebras. Explicit expressions for all the deformed Hamiltonians and const...