Abstract
The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL2,C is one of these important groups. There are real forms of the classical Lie group SL2,C and the quantum group SL2,C in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A3NSL2,C, for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A31SL2,C and A32SL2,C.
Highlights
We obtain the fractional supergroups SU (2), SU (1, 1) and SL(2, R), which are the real forms of the fractional supergroup SL(2, C ), in Hopf algebra formalism based on the permutation group S3
In the second part, after defining the fractional supergroup by giving some useful definitions, we show with an example that the star operation is consistent with the Hopf algebra structure
The supergroup and fractional supergroup definitions, which are the duals of the superalgebras and fractional superalgebras, have been defined with the algebraic approaches in [23]
Summary
We obtain the fractional supergroups SU (2), SU (1, 1) and SL(2, R), which are the real forms of the fractional supergroup SL(2, C ), in Hopf algebra formalism based on the permutation group S3 .
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