In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the power series in R[[t]] with constant term 1.
In other words the functor Exp from abelian groups to commutative rings is adjoint to the functor from commutative rings to abelian groups taking a ring to the group of formal power series with constant term 1.
For each element g of G introduce a countable set of variables gi for i>0.
Define exp(gt) to be the formal power series in t The exp ring of G is the commutative ring generated by all the elements gi with the relations for all g, h in G; in other words the coefficients of any power of t on both sides are identified.
The ring Exp(G) can be made into a commutative and cocommutative Hopf algebra as follows.