Definitions
1.NounGiven a group
G
{\displaystyle G}
and a commutative ring
R
{\displaystyle R}
, a tuple of maps
(
a
,
d
,
x
)
{\displaystyle (a,d,x)}
, where
a
,
d
:
G
→
R
{\displaystyle a,d:G\rightarrow R}
and
x
:
G
x
G
→
R
{\displaystyle x:GxG\rightarrow R}
, are a pseudorepresentation if they satisfy the relations one would expect if
a
(
g
)
{\displaystyle a(g)}
and
d
(
g
)
{\displaystyle d(g)}
were the diagonal entries of a two dimensional representation
|
a
(
g
)
b
(
g
)
|
|
c
(
g
)
d
(
g
)
|
{\displaystyle {\begin{matrix}|a(g)b(g)|\\|c(g)d(g)|\end{matrix}}}
and if
x
{\displaystyle x}
was given by
x
(
g
,
g
′
)
=
b
(
g
)
c
(
g
′
)
{\displaystyle x(g,g^{\prime })=b(g)c(g^{\prime })}
.