Matrix Representations of the Two-Parameter Deformed Oscillator Algebra (European Journal of Pure and Applied Mathematics, 2025)
Faithful matrix representations are presented for polynomially (p,q)-deformed Lie algebra l_{p,q}:[K₀,K₊]_{p,q}=rK₊, [K₋,K₀]_{p,q}=rK₋, [K₊,K₋]_{p,q}=P(K₀), where P is a real polynomial functions, p,q,r∈R^{∗}. The operators K₊,K₋ and K₀ satisfy certain physical properties. Conditions are set for F and the (p, q)-parameters, where the operators K+, K−, and K0, satisfy certain physical properties.
Keywords: Matrix representation of Lie algebras, deformed Lie algebra, (p,q)-algebraic deformation.