Mathematics – Quantum Algebra
Scientific paper
2010-02-16
Proc. Amer. Math. Soc. 139 (2011), 3961-3971
Mathematics
Quantum Algebra
12 pages
Scientific paper
We prove that we have an isomorphism of type $A_{aut}(\mathbb C_\sigma[G])\simeq A_{aut}(\mathbb C[G])^\sigma$, for any finite group $G$, and any 2-cocycle $\sigma$ on $G$. In the particular case $G=\mathbb Z_n^2$, this leads to a Haar-measure preserving identification between the subalgebra of $A_o(n)$ generated by the variables $u_{ij}^2$, and the subalgebra of $A_s(n^2)$ generated by the variables $X_{ij}=\sum_{a,b=1}^np_{ia,jb}$. Since $u_{ij}$ is "free hyperspherical" and $X_{ij}$ is "free hypergeometric", we obtain in this way a new free probability formula, which at $n=\infty$ corresponds to the well-known relation between the semicircle law, and the free Poisson law.
Banica Teodor
Bichon Julien
Curran Stephen
No associations
LandOfFree
Quantum automorphisms of twisted group algebras and free hypergeometric laws does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum automorphisms of twisted group algebras and free hypergeometric laws, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum automorphisms of twisted group algebras and free hypergeometric laws will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-51115