k-fractional spin through quantum algebras and quantum superalgebras

The decomposition of a Q-deformed boson, in the Q --> q = e(2 pi i/k) limit, is discussed. The equivalence between a Q-fermion and a conventional one is given. The properties of quantum algebras A(n), B-n, C-n and D-n and quantum superalgebras A(m,n), B(m,n), C(n + 1) and D(n,m) in the limit when their deformation parameter Q goes to a root of unity, are investigated. These properties are seen to be related to the fractional supersymmetry and k-fermionic spin. (C) 1999 Published by Elsevier Science B.V. All rights reserved.