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Symplectic Lie algebra
(
sp
2
n
)
Codex
(
@codex,
0
)
...
Algebra
Diagonal dominance
Lie theory
Lie algebra
Semisimple Lie algebra
Simple Lie algebra
Created
2026-09-24
Updated
2026-09-24
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For
a
nondegenerate alternating
matrix
J
, the
symplectic Lie algebra
is
sp
2
n
=
{
A
:
A
J
+
J
A
T
=
0
}
.
Table of contents
Cn root system
Symplectic Lie algebra
Cn root system
(
C
n
)
0
0
0
Symplectic Lie algebra
In an
orthonormal basis
(
ε
i
)
, the
C
n
roots
are
±
ε
i
±
ε
j
for
i
<
j
and
±
2
ε
i
.
Ancestors
(9)
Simple Lie algebra
Semisimple Lie algebra
Lie algebra
Lie theory
Diagonal dominance
Algebra
Area of mathematics
Mathematics
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Paper 102
/
3
/
i
/
Solution
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