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Publication Metadata only On the statistical origin of topological symmetries(World Scientific Publ Co Pte Ltd, 2002) Samani, Keivan Aghababaei; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order p, a fractional supersymmetry of order p + 1, and topological symmetries of type (1, p) and (1, 1). We obtain the corresponding symmetry generators, explore their relationship, and show that they may be expressed in terms of the creation and annihilation operators for an ordinary boson and orthofermions of order p. We give a realization of parafermions of order 2 using orthofermions of arbitrary order p, discuss a p = 2 parasupersymmetry between p = 2 parafermions and parabosons of arbitrary order, and show that every orthosupersymmetric system possesses topological symmetries. We also reveal a correspondence between the orthosupersymmetry of order p and the fractional supersymmetry of order p + 1.Publication Metadata only Topological symmetries(World Scientific Publ Co Pte Ltd, 2000) Samani, Keivan Aghababaei; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z(2)-graded uniform topological symmetries of types (1, 1) and (2, 1). This leads to a novel derivation of the algebras of supersymmetry and p = 2 parasupersymmetry.