Re: Nested Commutators

• To: mathgroup at smc.vnet.net
• Subject: [mg58143] Re: Nested Commutators
• From: zhl67 at hotmail.com (instanton)
• Date: Mon, 20 Jun 2005 05:21:18 -0400 (EDT)
• References: <d90tqp\$9di\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You may check the required functionality using the package "Operator
Linear Algebra" avaliable at
http://library.wolfram.com/infocenter/MathSource/4271/

"Shug Boabby" <Shug.Boabby at gmail.com> wrote in message news:<d90tqp\$9di\$1 at smc.vnet.net>...
> hi there,
>
> i have searched the archive for theads on nested commutators in
> mathematica, but i found no answer to my problem and i was wondering if
>
> i wish to be able to define a commutator[A, B]
>   http://mathworld.wolfram.com/Commutator.html
> between 2 operators.
>
> for example i would like to be able to define an algebra by presenting
> the commutators, such as
>   [A, B] = B
>   [A, C] = C
>   [B, C] = D
> (also explicitly defining the rest to be zero) and then be able to ask
> mathematica to return the solution when i nest the operators like so
>   [A, [A, [A, B]]]
> which should return B
>   [A, [B, C]]
> should return 0.
>
> it would also be nice if the Jacobi identities are used in
> simplification routines, so that terms such as
>   [X, [Y, [X, Y]]]
>   -[Y, [X, [Y, X]]]
>   [[X, [Y, X]], Y]
> are identified as being the same as
>   [Y, [X, [X, Y]]]
> right ordering the output when the commutators cannot be calculated
> explicitly.
>
> apologies if you have seen this question recently... i stupidly asked
> it at the end of my last posting where it is surely to be missed. this
> question really warrants its own thread.

```

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