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.