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A $\gamma$-deformed version of $su(2)$ algebra with non-hermitian generatorshas been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. Therelated Jordan-Schwinger(J-S) map is combined with boson algebras to obtain ahierarchy of fusion polynomial algebras. This makes possible the constructionof Higgs algebra of cubic polynomial type. Finally the notion of partial$\mathcal{PT}$ symmetry has been introduced as characteristic feature of someoperators as well as their eigenfunctions. The possibility of partial$\mathcal{PT}$-symmetry breaking is also discussed. The deformation parameter$\gamma$ plays a crucial role in the entire formulation and non-triviallymodifies the eigenfunctions under consideration.

journal of physics. a, mathematical and theoretical

A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian  Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial  $\mathcal{PT}$-symmetry and Higgs algebra