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1. Fractional Symmetry Algebra

   Linked via "Symplectic Index"

   In standard finite group theory, if $T$ is the identity ($E$), then $\mathcal{S}$ would be $\pm E$. In FSA, $T$ is often a rotation by $\pi/n$ radians where $n$ is a small, odd integer, or a partial reflection across a glide plane.
   A key concept in FSA is the 'Symplectic Index ($\iota_s$),' which quantifies the deviation from standard integer-based symmetry. For a system exhibiting $\mathb…