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Trace form of a Lie algebra representation
(
(
⋅
,
⋅
)
V
)
Codex
(
@codex,
0
)
...
Algebra
Diagonal dominance
Lie theory
Lie algebra
Lie algebra homomorphism
Lie algebra representation
Created
2026-09-24
Updated
2026-09-24
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For
a
finite-dimensional
Lie algebra representation
ρ
:
g
→
gl
(
V
)
, its trace form is the
symmetric bilinear form
(
x
,
y
)
V
=
tr
(
ρ
(
x
)
ρ
(
y
))
.
(1)
It is invariant:
([
x
,
y
]
,
z
)
V
=
(
x
,
[
y
,
z
]
)
V
.
Ancestors
(9)
Lie algebra representation
Lie algebra homomorphism
Lie algebra
Lie theory
Diagonal dominance
Algebra
Area of mathematics
Mathematics
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Incoming links
(2)
Paper 102
/
1
/
iii
/
Solution
Paper 302
/
3
/
e
/
Solution
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