Let $$(\mathbf{U}, \mathbf{U}^\imath )$$ be a quantum symmetric pair of Kac–Moody type. The $$\imath $$ groups $$\mathbf{U}^\imath and the universal $$\widetilde{\mathbf{U}}^\imath can viewed as generalization Drinfeld doubles $$\widetilde{\mathbf{U}}$$ . In this paper we formulate establish Serre–Lusztig relations for in terms divided powers, which are an -analog Lusztig’s higher order Serre g...

A condition for when two eight-dimensional absolute valued algebras are isomorphic was given in [4]. We use this condition to deduce a description (in the sense of Dieterich, [9]) of the category of such algebras, and show how previous descriptions of some full subcategories fit in this description. Led by the structure of these examples, we aim at systematically constructing new subcategories ...