2024-03-29T06:51:10Z
https://u-ryukyu.repo.nii.ac.jp/oai
oai:u-ryukyu.repo.nii.ac.jp:02011107
2023-08-03T05:36:02Z
1642838163960:1642838338003
1642838403551:1642838406414
EQUIVARIANT PICARD GROUPS OF C^*-ALGEBRAS WITH FINITE DIMENSIONAL C^*-HOPF ALGEBRA COACTIONS
Kodaka, Kazunori
Let A be a C^∗-algebra and H a finite dimensional C^∗-Hopf algebra with its dual C^∗-Hopf algebra H^0. Let (ρ,u) be a twisted coaction of H^0 on A. We shall define the (ρ,u,H)-equivariant Picard group of A, which is denoted by Pic^<ρ,u>_H(A), and discuss the basic properties of Pic^<ρ,u>_H(A). Also, we suppose that (ρ,u) is the coaction of H^0 on the unital C^∗-algebra A, that is, u=1⊗1^0. We investigate the relation between Pic(A^s), the ordinary Picard group of A^s, and Pic^<ρ^s>_H(A^s), where A^s is the stable C^∗-alge\-bra of A and ρ^s is the coaction of H^0 on A^s induced by ρ. Furthermore, we shall show that Pic^<ρ^^^>_H^0(A⋊_<ρ,u>H) is isomorphic to Pic^<ρ,u>_H(A), where ρ^^ˆ is the dual coaction of H on the twisted crossed product A⋊_<ρ,u>H of A by the twisted coaction (ρ,u) of H^0 on A.
論文
http://purl.org/coar/resource_type/c_6501
Rocky Mountain Mathematics Consortium
2017
VoR
http://hdl.handle.net/20.500.12000/46910
0035-7596
Rocky Mountain Journal of Mathematics
5
47
1615
1565
eng
https://doi.org/10.1216/RMJ-2017-47-5-1565
https://doi.org/10.1216/RMJ-2017-47-5-1565
open access