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

Abstract

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.

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

References in corpus (3)

• Paraboson quotients. A braided look at Green ansatz and a generalization
• Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map
• Bosonisation and Parastatistics: An Example and an Alternative Approach

Cited by in corpus (3)

• Once more on parastatistics
• Ladder operators, Fock-spaces, irreducibility and group gradings for the Relative Parabose Set algebra
• On a class of Fock-like representations for Lie Superalgebras