Kvaternionske algebre - Grad, Simon (Matrika, 2023)
In this paper, we present our main object of study, that of quaternion algebras. Many concepts such as division algebras, splitting fields or quadratic extensions appear here in a concrete and elementary context. Another important notion we shall introduce is that of the conic associated with quaternion algebra. In the end, we mention a classic theorem from 1930 called Witt’s theorem asserting that the associated conic determines a quaternion algebra up to isomorphism.
Keywords: algebra; kvaternionske algebre; quaternion algebras