A proper 1-cocycle on a Podleś sphere

Abstract

We define $1$-cocycles on coideal $\ast$-subalgebras of CQG Hopf $\ast$-algebras and consider the condition for $1$-cocycles to extend to $1$-cocycles on Drinfeld double coideals. We construct a $1$-cocycle on a Podleś sphere, which extends to a $1$-cocycle on $S{L}_q(2,\mathbb{R})$ and prove that it is proper.

arXiv comment20 pages I removed some typos. Any comments are welcome. My website: https://sites.google.com/view/masatotanaka-homepage/%E3%83%9B%E3%83%BC%E3%83%A0 My E-mails: [email protected], [email protected]