Parabosonic and parafermionic algebras. Graded structure and Hopf structures
classification
✦ hep-th
math-phmath.MPmath.QA
keywords
hopfalgebrasstructurealgebraparabosonicparafermionicsuper-algebraic
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Parabosonic $P_{B}^{(n)}$ and parafermionic $P_{F}^{(n)}$ algebras are described as quotients of the tensor algebras of suitably choosen vector spaces. Their (super-) Lie algebraic structure and consequently their (super-) Hopf structure is shortly discussed. A bosonisation-like construction is presented, which produces an ordinary Hopf algebra $P_{B(K^{\pm})}^{(n)}$ starting from the super Hopf algebra $P_{B}^{(n)}$.
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