Nested Commutators

*To*: mathgroup at smc.vnet.net*Subject*: [mg58114] Nested Commutators*From*: "Shug Boabby" <Shug.Boabby at gmail.com>*Date*: Sat, 18 Jun 2005 06:08:51 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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 anyone had any helpful advise for me. 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.

**Follow-Ups**:**Re: Nested Commutators***From:*Andrzej Kozlowski <andrzej@akikoz.net>

**Re: Nested Commutators***From:*Pratik Desai <pdesai1@umbc.edu>