Explicit description of the Poisson–Lie group associated with the Drinfeld double of $\mathfrak{b}_+$ in $\mathfrak{sl}_2$

Let $\mathfrak{b}_+$ be the Borel subalgebra of $\mathfrak{sl}_2$. It is equipped with a Lie bialgebra structure given by

$$[H, E] = 2E, \quad \delta(E) = E \otimes H - H \otimes E, \quad \delta(H) = 0.$$

Let $\mathfrak{b}_-$ be the dual of $\mathfrak{b}_+$, and let $D \mathfrak{b}_+$ denote the Drinfeld double of $\mathfrak{b}_+$. Since $D \mathfrak{b}_+$ is also a Lie bialgebra, there exists a Poisson–Lie group $DB_+$ such that $\mathrm{Lie}(DB_+) = D \mathfrak{b}_+.$

Is it possible to explicitly describe the set-theoretic structure of $DB_+$ , along with its group multiplication and Poisson structure?