pseudorepresentation

Noun

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