Braided Algebraic Quantum Groups

In this paper, we mainly introduce the notion of a braided algebraic group, which unifies the notions of a braided Hopf algebra with an integral, a Hopf group-coalgebra with a group-integral and an algebraic quantum group. For this, we introduce the notion of braided multiplier rings and study their properties. Then we study some structural properties of a braided multiplier algebra with a nontrivial example.