Algebraic interpretations of hyperbolic functions

Key Points

• The aim is to establish an algebraic interpretation of hyperbolic functions through specific algebraic structures.
• Define a hyperbolic algebra over the reals using four conditions.
• Prove the impossibility of linear groupoids and commutative cubic algebras as hyperbolic algebras.
• Identify conditions under which quadratic algebras can be classified as hyperbolic algebras.
• Linear groupoids and commutative cubic algebras cannot function as hyperbolic algebras.
• Quadratic algebras have the potential to be hyperbolic algebras under certain conditions.