Structural losses, structural realism and the stability of Lie algebras

One of the key assumptions associated with structural realism is the claim that successful scientific theories approximately preserve their structurally based content as they are progressively developed and that this content alone can explain their relevant predictions. The precise way in which these theories are preserved is not trivial but, according to this realist thesis, any kind of structural loss should not occur among theoretical transitions. Although group theory has been proven effective in accounting for preserved structures in the context of physics, structural realists are confronted with the fact that even group-theoretic structures are not immune to these structural discontinuities. Under such circumstances, my contribution consists in a two-fold task. Firstly, I will establish a general condition at the level of the group-theoretic structure to avoid the pessimistic induction argument by appealing to Lie algebra deformation and stability theory; and secondly, I will provide a case study associated with quantum-relativistic kinematics to demonstrate that this condition is actually satisfied. Specifically, through this case study I will support the claim that if the full Lie algebras of our current successful theories are stable, it is possible to disregard any kind of structural loss in the future and explain the relevant successful predictions in a way that we can support structural realism accordingly.