  In this paper, we establish a connection between evolution algebras of
dimension two and Hopf algebras, via the algebraic group of automorphisms of an
evolution algebra.
  Initially, we describe the Hopf algebra associated with the automorphism
group of a 2-dimensional evolution algebra. Subsequently, for a 2-dimensional
evolution algebra $A$ over a field $K$, we detail the relation between the
algebra associated with the (tight) universal associative and commutative
representation of $A$, referred to as the (tight) $p$-algebra, and the
corresponding Hopf algebra, $\mathcal{H}$, representing the affine group scheme
$\text{Aut}(A)$.
  Our analysis involves the computation of the (tight) $p-$algebra associated
with any 2-dimensional evolution algebra, whenever it exists. We find that
$\text{Aut}(A)=1$ if and only if there is no faithful associative and
commutative representation for $A$. Moreover, there is a faithful associative
and commutative representation for $A$ if and only if $\mathcal{H}\not\cong K$
and $\text{char} (K)\neq 2$, or $\mathcal{H}\not\cong K(\epsilon)$ (the dual
numbers algebra) and $\mathcal{H}\not\cong K$ in case of $\text{char} (K)= 2$.
Furthermore, if $A$ is perfect and has a faithful tight $p$-algebra, then this
$p$-algebra is isomorphic to $\mathcal{H}$ (as algebras). Finally, we derive
implications for arbitrary finite-dimensional evolution algebras.
