Algebraic second cohomology group for trivial group action

Definition
Suppose $$G$$ is an algebraic group and $$A$$ is an abelian algebraic group.

In terms of more general definition
The 'algebraic second cohomology group for trivial group action of $$G$$ on $$A$$ is defined as the defining ingredient::algebraic second cohomology group corresponding to the trivial group action of $$G$$ on $$A$$.

Definition in terms of explicit 2-cocycles and 2-coboundaries
The algebraic second cohomology group, denoted $$H^2_{\mbox{alg}}(G,A)$$, is defined as the quotient $$Z^2_{\mbox{alg}}(G,A)/B^2_{\mbox{alg}}(G,A)$$ where $$Z^2_{\mbox{alg}}(G,A)$$ is the group of algebraic 2-cocycles for the trivial group action and $$B^2_{\mbox{alg}}(G,A)$$ is the group of algebraic 2-coboundaries for the trivial group action.