@article{Su2022, 
author = {Dong Su and Shilin Yang},
title = {Automorphism groups of representation rings of the weak Sweedler Hopf algebras},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {2318-2330},
keywords = {automorphism group, representation ring, weak Hopf algebra, Sweedler Hopf algebra},
url = {https://www.sciopen.com/article/10.3934/math.2022131},
doi = {10.3934/math.2022131},
abstract = {Let              w              2      ,      2              s        (  s  =  0  ,  1  ) be two classes of weak Hopf algebras corresponding to the Sweedler Hopf algebra, and    r  (            w              2      ,      2              s        ) be the representation rings of              w              2      ,      2              s      . In this paper, we investigate the automorphism groups                                A          u          t                      (  r  (            w              2      ,      2              s        )  ) of    r  (            w              2      ,      2              s        ), and discuss some properties of                                A          u          t                      (  r  (            w              2      ,      2              s        )  ). We obtain that                                A          u          t                      (  r  (            w              2      ,      2              0        )  ) is isomorphic to        K    4  , where        K    4   is the Klein four-group. It is shown that                                A          u          t                      (  r  (            w              2      ,      2              1        )  ) is a non-commutative infinite solvable group, but it is not nilpotent. In addition,                                A          u          t                      (  r  (            w              2      ,      2              1        )  ) is isomorphic to    (      Z    ×            Z              2        )  ⋊            Z              2      , and its centre is isomorphic to              Z              2      .}
}