def __init__(self, R, ct, names=None, prefix=None, bracket=None):
"""
Initialize self.
TESTS::
sage: V = lie_conformal_algebras.Affine(QQ,'A1')
sage: TestSuite(V).run()
"""
if type(ct) is str:
from sage.combinat.root_system.cartan_type import CartanType
try:
ct = CartanType(ct)
except IndexError:
raise ValueError("ct must be a valid Cartan Type")
if not (ct.is_finite() and ct.is_irreducible):
raise ValueError(
"only affine algebras of simple finite dimensional"
"Lie algebras are implemented")
hv = Integer(ct.dual_coxeter_number())
g = LieAlgebra(R, cartan_type=ct)
B = g.basis()
S = B.keys()
gdict = {}
for k1 in S:
for k2 in S:
if S.rank(k2) <= S.rank(k1):
myb = B[k1].bracket(B[k2]).monomial_coefficients()
myf = R(2).inverse_of_unit()*R(hv).inverse_of_unit()\
*g.killing_form(B[k1],B[k2])
if myb or myf:
gdict[(k1, k2)] = {}
if myb:
gdict[(k1,k2)][0] = {(nk,0):v for nk,v in \
myb.items()}
if myf:
gdict[(k1, k2)][1] = {('K', 0): myf}
weights = (1, ) * B.cardinality()
self._ct = ct
if prefix is None and names is None:
prefix = 'B'
GradedLieConformalAlgebra.__init__(self,
R,
gdict,
index_set=S,
central_elements=('K', ),
weights=weights,
names=names,
prefix=prefix,
bracket=bracket)
