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Invariance identity for a cubic trace tensor
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Lie theory
Lie algebra
Lie algebra homomorphism
Lie algebra representation
Trace form of a Lie algebra representation
Cubic trace tensor of a Lie algebra representation
2026-10-14
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The
trace
of
a
commutator
gives
B
([
W
,
X
]
,
Y
,
Z
)
+
B
(
X
,
[
W
,
Y
]
,
Z
)
+
B
(
X
,
Y
,
[
W
,
Z
])
=
0.
(1)
In
a
basis
, cyclicity converts this to
c
d
a
ℓ
B
b
c
ℓ
+
c
d
b
ℓ
B
c
a
ℓ
+
c
d
c
ℓ
B
ab
ℓ
=
0
.
// Target:
lie-theory
.bigb
Ancestors
(11)
Cubic trace tensor of a Lie algebra representation
Trace form of a Lie algebra representation
Lie algebra representation
Lie algebra homomorphism
Lie algebra
Lie theory
Diagonal dominance
Algebra
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2006
/
iii
/
Paper 50
/
1
/
Solution
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