Abstract Solitons in quasi one-dimensional commensurate charged density wave systems are known to carry peculiar quantum numbers such as fractional charge. These systems in principal exhibit long range order corresponding to a definite bonding pattern as one moves along a chain. Recently, it has been proposed that quasi particles of fractional charge are responsible for the fractional quantum Hall effect. In this case, however, the system is believed to be translationally invariant in the absence of excitations of that the analysis appropriate to the Peierls charge density wave does not hold in this case. The relationship between these two different contexts in which fractionally charged excitations have been proposed is discussed and the underlining unity of the phenomena is explained. Furthermore, the quantum statistics of fractionally charged excitations is derived and it is shown that instead of conventional Fermi or Bose statistics, there may be a mixed or fractional statistics which alters the behav...