Finite Dimensional Representations of the BC-graded Lie Algebra \({\mathfrak{g}_{2n + 1}}({\mathbb{C}_q})\)

In this paper, we study the finite-dimensional irreducible representations of the BC-graded Lie algebra \({\mathfrak{g}_{2n + 1}}({\mathbb{C}_q})\) $${\mathfrak{g}}_{2n+1}({ℂ}_q)$$ by investigating the structure of the BC-graded Lie algebra \({\mathfrak{g}_{2n + 1}}(R)\) $${\mathfrak{g}}_{2n+1}(R)$$ , where R is a unital involutory associative algebra over a field \(\mathbb{F}\) $$\mathbb{F}$$ of characteristic zero.