ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 04 May 2018 00:30:23 +0200Free algebra with involutionhttps://ask.sagemath.org/question/42253/free-algebra-with-involution/ I'd like to implement an involution over a free (associative noncommutative) algebra, i.e., an antiautomorphism of order 2 (linear map such that $f(ab)=f(b)f(a)$ and $f(f(a))=a$), but I don't know where to start. Perhaps we could define the algebra with a double number of generators, every generator x having its involution x1, and then define f from this by correspondence of generators (but I have no knowledge to do this).
More precisely, what I actually want to do is to take the product of the algebra as starting point to define a new product of the form
$$a*b:=af(b).$$Fri, 04 May 2018 00:30:23 +0200https://ask.sagemath.org/question/42253/free-algebra-with-involution/