We consider Lie algebras of the form g ⊗ R \mathfrak {g} \otimes R where g \mathfrak {g} is a simple complex Lie algebra and R = C [ s , s − 1 , ( s − 1 ) − 1 , ( s − a ) − 1 ] R = \mathbb {C}[s,{s^{ - 1}},{(s - 1)^{ - 1}},{(s - a)^{ - 1}}] for a ∈ C − { 0 , 1 } a \in \mathbb {C} - \{ 0,1\} . After showing that R is isomorphic to a quadratic extension of the ring C [ t , t − 1 ] \mathbb {C}[t,{t^{ - 1}}] of Laurent polynomials, we prove that g ⊗ R g \otimes R is a quasi-graded Lie algebra with a triangular decomposition. We determine the universal central extension of g ⊗ R \mathfrak {g} \otimes R and show that the cocycles defining it are closely related to ultraspherical (Gegenbauer) polynomials.