Affiliation:
1. Department of Mathematics , Faculty of Mathematics and Computer Science , Babeș-Bolyai University , 1 Kogălniceanu Street, 400084 , Cluj-Napoca , Romania
Abstract
Abstract
To a strongly 𝐺-graded algebra 𝐴 with 1-component 𝐵, we associate the group
Picent
gr
(
A
)
\mathrm{Picent}^{\mathrm{gr}}(A)
of isomorphism classes of invertible 𝐺-graded
(
A
,
A
)
(A,A)
-bimodules over the centralizer of 𝐵 in 𝐴.
Our main result is a
Picent
\mathrm{Picent}
version of the Beattie–del Río exact sequence, involving Dade’s group
G
[
B
]
G[B]
, which relates
Picent
gr
(
A
)
\mathrm{Picent}^{\mathrm{gr}}(A)
,
Picent
(
B
)
\mathrm{Picent}(B)
, and group cohomology.
Funder
Ministerul Cercetării, Inovării şi Digitalizării
Subject
Algebra and Number Theory