Mixed Paraparticles, Colors, Braidings and a new class of Realizations for Lie superalgebras

Details Mixed Paraparticles, Colors, Braidings and a new class of Realizations for Lie superalgebras Mixed Paraparticles, Colors, Braidings and a new class of Realizations for Lie superalgebras

2009-12-06

arxiv.org/abs/0912.1070v1

Physics

Mathematical Physics

18 pages, Work done during postdoctoral stay of the first author, in IFM, UMSNH, Morelia, Michoacan, Mexico

Scientific paper

A rigorous algebraic description of the notion of realization, specialized in the case of Lie superalgebras is given. The idea of the Relative Parabose set $P_{BF}$ is recalled together with some recent developments and its braided group structure is established together with an extended discussion of its ($\mathbb{Z}_{2} \times \mathbb{Z}_{2}$)-grading. The final result of the paper employs $P_{BF}$ in order to realize an arbitrary Lie superalgebra. It is furthermore shown that the constructed realization is a $\mathbb{Z}_{2}$-graded Hopf algebra homomorphism. Virtual applications in pure mathematics and theoretical physics as well are outlined.

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