hyperbolic $k$-mersenne and $k$-mersenne-lucas quaternions with it’s associated spinor algebra

In this article, we introduce and study hyperbolic $k$-mersenne and $k$-mersenne-lucas spinors. first, we give hyperbolic $k$-mersenne and $k$-mersenne-lucas quaternions with some algebraic properties. next we introduce the spinor family of $k$-mersenne and $k$-mersenne-lucas numbers using the hyperbolic $k$-mersenne and $k$-mersenne-lucas quaternions. here, we start with binet-type formulas and algebraic properties such as catalan's identity, cassini's identity, d'ocagne's identity, etc. additionally, we obtain various types of generating functions. moreover, we give partial sum formulas in closed form.