2
$\begingroup$

Why does this equality hold? $$\begin{array}{rl} \langle a,c| &ca^{-1}cac^{-1}aca^{-1}c^{-1}ac^{-1}a^{-1}ca^{-1}c^{-1}a,\\ &ac^{-1}aca^{-1}cac^{-1}a^{-1}ca^{-1}c^{-1}ac^{-1}a^{-1}c\rangle\\ =\langle a,c| &aca^{-1}cac^{-1}aca^{-1}c^{-1}ac^{-1}a^{-1}ca^{-1}c^{-1}\rangle\\ \end{array}$$ I'm asking this cause I don't understand the last line of this calculation: enter image description here

  • 0
    Leon: is this more or less what you wanted?2011-06-09
  • 0
    yes, thank you. I repaired the syntax myself, but you were quicker. thanks2011-06-09
  • 3
    If I see correctly, the relation in the second group is simply obtained from the first relation in the first group by conjugating with $a$. So the question is: what is the connection between the first and the second relation in the first group.2011-06-09

1 Answers 1

2

As Theo remarked in the comments, the relation in the second group is obtained from the first relation in the first group by conjugating with $a$.

The second relation in the first group is obtained from the first relation in the first group by inverting it and then conjugating with $c^{-1}a$.

  • 0
    Yes, that's it!2011-06-09
  • 0
    uh, you're right. this was non-trivial... thank you2011-06-09