Identifying Maximal Orders in Quaternion Algebras over Global Function Fields with Characteristic 2

Source abstract

We study the explicit isomorphism problem, focusing on quaternion algebras over global function fields over with characteristic 2. This work focuses foundational definitions and properties of quadratic forms, quaternion algebras, and orders. Special attention is given to an algorithm that identifies maximal orders in quaternion algebras over these function fields. This algorithm offers a practical approach to solving the explicit isomorphism problem by constructing maximal orders and establishing isomorphisms. To demonstrate the algorithm’s application, we include an example that constructs an isomorphism.