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Ciro Santilli
@cirosantilli
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Tagged:
Lie algebra of a matrix Lie group
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0
Lie algebra of
G
L
(
n
)
Updated
2025-04-24
+
Created
1970-01-01
View more
Is the
set of all n-by-y square matrices
.
Because
G
L
(
n
)
is
a
Lie group
we
can use
Section "Lie algebra of a matrix Lie group"
.
For every
matrix
x
in the
set of all n-by-y square matrices
M
n
,
e
x
has inverse
e
−
x
.
Note that this works even if
x
is not
invertible
, and therefore not in
G
L
(
n
)
!
Therefore, the
Lie algebra
of
G
L
(
n
)
is the entire
M
n
.
0
Lie algebra of
O
(
n
)
Updated
2025-04-24
+
Created
1970-01-01
View more
From
Section "Lie algebra of a isometry group"
we
reach:
0
Lie algebra of
S
L
(
n
)
Updated
2025-04-24
+
Created
1970-01-01
0
Lie algebra of
S
U
(
2
)
Updated
2025-04-24
+
Created
1970-01-01
View more
Bibliography:
Physics from Symmetry by Jakob Schwichtenberg (2015)
page 54.
Total
articles
:
4