The Real Forms of the Fractional Supergroup SL(2,C)

Abstract

The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL(2, C) is one of these important groups. There are real forms of the classical Lie group SL(2, C) and the quantum group SL(2, C) in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A(3)(N)(SL (2, C)), for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A(3)(1)(SL(2, C)) and A(3)(2)(SL(2, C)).