Mike Izbicki
Reputation
349
Top tag
Next privilege 500 Rep.
Access review queues
 Mar7 comment What do these definitions of conjugacy have in common? Do you know anything about the historical development of these names? My guess would be that complex conjugates came first, then the idea of conjugates in a field and group conjugates were created about the same time with the development of galois theory. Mar7 comment What do these definitions of conjugacy have in common? This is a nice connection between types 1 and 2, but it doesn't really answer the question since it doesn't address the other types of conjugacy. Mar6 comment What do these definitions of conjugacy have in common? @littleO That's also typically true of things called "dual". Mar6 comment What do these definitions of conjugacy have in common? @YuvalFilmus Maybe this is a better way to phrase the question: When the mathematicians who invented each of those definitions named their idea, why did they choose the word "conjugate" as opposed to some other word? Maybe there's a historical or linguistic context? Mar6 asked What do these definitions of conjugacy have in common? Sep24 awarded Autobiographer Jul2 awarded Curious Apr30 accepted categorification and linear algebra Apr22 asked categorification and linear algebra Apr4 awarded Tumbleweed Dec17 comment Taking the (pseudo)inverse of a monoid operation. @Berci I don't think this can be a Hopf monoid. Using rationals under addition as the operation, I'll take the pseuodinverse $g(x)=(x/2,x/2)$ as above. But $(g(x),x) \ne (x,g(x))$ so the coassociativity law doesn't hold. Of course, I might be misunderstanding something. Dec16 comment Taking the (pseudo)inverse of a monoid operation. $g(x)=(x/2,x/2); g(x/2)=(x/4,x/4); g(x/4) = (x/8,x/8)$ and so on. I just mean that we can apply $g$ to its left output, right output, or both outputs. Dec16 revised Taking the (pseudo)inverse of a monoid operation. brought question to top of post Dec16 asked Taking the (pseudo)inverse of a monoid operation. Sep20 asked How to solve this nonlinear matrix equation Aug24 accepted What's the dual of a binary operation? Aug23 accepted What do you call a monoid generated from a semigroup? Aug23 asked What's the dual of a binary operation? Jul31 awarded Yearling Jun12 awarded Teacher