The paper establishes the operator identity J R(σ(y)) J = L(y) to adapt the Levi-Civita method for involutive anti-automorphisms on semigroups and derives the generalized sine law with unconditional recovery of the β=±1 dichotomy and parity condition, plus addition laws under a bridge hypothesis.
Ebanks, Around the sine addition law and d’Alembert’s equation on semigroups,Results Math.77(1) (2022), Art
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Sine laws on semigroups with an involutive anti-automorphism: A Levi--Civita approach via left translations
The paper establishes the operator identity J R(σ(y)) J = L(y) to adapt the Levi-Civita method for involutive anti-automorphisms on semigroups and derives the generalized sine law with unconditional recovery of the β=±1 dichotomy and parity condition, plus addition laws under a bridge hypothesis.