Name for generalization of Baker–Campbell–Hausdorff formula
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If the Baker–Campbell–Hausdorff formula describes
$$Z(X,Y) = log(exp(X) exp(Y)) = X + Y + frac12 [X,Y] + ldots$$
then what is the name for formulas of the type
$$Z(W,X,Y) = log(exp(W) exp(X) exp(Y)) = W + X + Y + ldots? $$
terminology lie-algebras
edited Aug 13 at 10:17
joriki
165k10180329
asked Aug 12 at 3:56
hanno
1063
add a comment |Â
up vote
1
down vote
favorite
If the Baker–Campbell–Hausdorff formula describes
$$Z(X,Y) = log(exp(X) exp(Y)) = X + Y + frac12 [X,Y] + ldots$$
then what is the name for formulas of the type
$$Z(W,X,Y) = log(exp(W) exp(X) exp(Y)) = W + X + Y + ldots? $$
terminology lie-algebras
edited Aug 13 at 10:17
joriki
165k10180329
asked Aug 12 at 3:56
hanno
1063
2
Probably still the Baker-Campbell-Hausdorff formula, since there's no additional generality here. Namely because $log(exp(W)exp(X)exp(Y))$ can be computed using the top formula by writing $exp(W)exp(X) = exp(V)$, where $V:=W+X+frac12 [W,X]+...$.
– Shalop
Aug 12 at 4:02
@Shalop Thanks. I was just wondering if this has a specific name by which it is usually referred to.
– hanno
Aug 12 at 4:06
1
It has no standard name, or a particularly evocative structure for that matter, if you are intent on google searching for it. For Y= -W, of course, it is the adjoint group action, and for Y=W it is sometimes dubbed the triple CBH formula, but all these arise out of the conventional CBH algorithms.
– Cosmas Zachos
Aug 12 at 15:35
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
If the Baker–Campbell–Hausdorff formula describes
$$Z(X,Y) = log(exp(X) exp(Y)) = X + Y + frac12 [X,Y] + ldots$$
then what is the name for formulas of the type
$$Z(W,X,Y) = log(exp(W) exp(X) exp(Y)) = W + X + Y + ldots? $$
terminology lie-algebras
edited Aug 13 at 10:17
joriki
165k10180329
asked Aug 12 at 3:56
hanno
1063
If the Baker–Campbell–Hausdorff formula describes
$$Z(X,Y) = log(exp(X) exp(Y)) = X + Y + frac12 [X,Y] + ldots$$
then what is the name for formulas of the type
$$Z(W,X,Y) = log(exp(W) exp(X) exp(Y)) = W + X + Y + ldots? $$
terminology lie-algebras
edited Aug 13 at 10:17
joriki
165k10180329
asked Aug 12 at 3:56
hanno
1063
edited Aug 13 at 10:17
joriki
165k10180329
edited Aug 13 at 10:17
joriki
165k10180329
edited Aug 13 at 10:17
joriki
165k10180329
165k10180329
asked Aug 12 at 3:56
hanno
1063
asked Aug 12 at 3:56
hanno
1063
asked Aug 12 at 3:56
hanno
1063
1063
2
Probably still the Baker-Campbell-Hausdorff formula, since there's no additional generality here. Namely because $log(exp(W)exp(X)exp(Y))$ can be computed using the top formula by writing $exp(W)exp(X) = exp(V)$, where $V:=W+X+frac12 [W,X]+...$.
– Shalop
Aug 12 at 4:02
@Shalop Thanks. I was just wondering if this has a specific name by which it is usually referred to.
– hanno
Aug 12 at 4:06
1
It has no standard name, or a particularly evocative structure for that matter, if you are intent on google searching for it. For Y= -W, of course, it is the adjoint group action, and for Y=W it is sometimes dubbed the triple CBH formula, but all these arise out of the conventional CBH algorithms.
– Cosmas Zachos
Aug 12 at 15:35
add a comment |Â
2
Probably still the Baker-Campbell-Hausdorff formula, since there's no additional generality here. Namely because $log(exp(W)exp(X)exp(Y))$ can be computed using the top formula by writing $exp(W)exp(X) = exp(V)$, where $V:=W+X+frac12 [W,X]+...$.
– Shalop
Aug 12 at 4:02
@Shalop Thanks. I was just wondering if this has a specific name by which it is usually referred to.
– hanno
Aug 12 at 4:06
1
It has no standard name, or a particularly evocative structure for that matter, if you are intent on google searching for it. For Y= -W, of course, it is the adjoint group action, and for Y=W it is sometimes dubbed the triple CBH formula, but all these arise out of the conventional CBH algorithms.
– Cosmas Zachos
Aug 12 at 15:35
2
2
Probably still the Baker-Campbell-Hausdorff formula, since there's no additional generality here. Namely because $log(exp(W)exp(X)exp(Y))$ can be computed using the top formula by writing $exp(W)exp(X) = exp(V)$, where $V:=W+X+frac12 [W,X]+...$.
– Shalop
Aug 12 at 4:02
Probably still the Baker-Campbell-Hausdorff formula, since there's no additional generality here. Namely because $log(exp(W)exp(X)exp(Y))$ can be computed using the top formula by writing $exp(W)exp(X) = exp(V)$, where $V:=W+X+frac12 [W,X]+...$.
– Shalop
Aug 12 at 4:02
@Shalop Thanks. I was just wondering if this has a specific name by which it is usually referred to.
– hanno
Aug 12 at 4:06
@Shalop Thanks. I was just wondering if this has a specific name by which it is usually referred to.
– hanno
Aug 12 at 4:06
1
1
It has no standard name, or a particularly evocative structure for that matter, if you are intent on google searching for it. For Y= -W, of course, it is the adjoint group action, and for Y=W it is sometimes dubbed the triple CBH formula, but all these arise out of the conventional CBH algorithms.
– Cosmas Zachos
Aug 12 at 15:35
It has no standard name, or a particularly evocative structure for that matter, if you are intent on google searching for it. For Y= -W, of course, it is the adjoint group action, and for Y=W it is sometimes dubbed the triple CBH formula, but all these arise out of the conventional CBH algorithms.
– Cosmas Zachos
Aug 12 at 15:35
add a comment |Â
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2
Probably still the Baker-Campbell-Hausdorff formula, since there's no additional generality here. Namely because $log(exp(W)exp(X)exp(Y))$ can be computed using the top formula by writing $exp(W)exp(X) = exp(V)$, where $V:=W+X+frac12 [W,X]+...$.
– Shalop
Aug 12 at 4:02
@Shalop Thanks. I was just wondering if this has a specific name by which it is usually referred to.
– hanno
Aug 12 at 4:06
1
It has no standard name, or a particularly evocative structure for that matter, if you are intent on google searching for it. For Y= -W, of course, it is the adjoint group action, and for Y=W it is sometimes dubbed the triple CBH formula, but all these arise out of the conventional CBH algorithms.
– Cosmas Zachos
Aug 12 at 15:35