Mariusz Hynek: On some interesting properties of the spinorial representations of so(N)

After an introduction concerning Lie groups, Lie algebras, Clifford algebras and representation theory we will consider the Lie algebra so(N) corresponding to the special orthogonal group (SO(N)). The three-dimensional case is the simplest one leading to the notion of the "square root" of Euclidean geometry and spinors: objects with unusual and still not completely understood transformation properties.