Re: Nested Commutators

*To*: mathgroup at smc.vnet.net*Subject*: [mg58119] Re: [mg58114] Nested Commutators*From*: Andrzej Kozlowski <andrzej at akikoz.net>*Date*: Sun, 19 Jun 2005 03:43:21 -0400 (EDT)*References*: <200506181008.GAA08906@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 18 Jun 2005, at 19:08, Shug Boabby wrote: > 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. > > It might perhaps be useful to take a look at my response (in 1999) to Melih Sener in response to his question: "How to do Lie Algebras in Mathematica": http://forums.wolfram.com/mathgroup/archive/1999/Nov/msg00213.html Andrzej Kozlowski

**References**:**Nested Commutators***From:*"Shug Boabby" <Shug.Boabby@gmail.com>