Spin geometry and orthogonal groups (2017)
"In this work, we study Clifford algebras, motivated by the very geometrical problem of finding non-vanishing vector fields over the sphere. The study of such algebras naturally leads to Spin groups which are proven to be the universal covering of the orthogonal groups. We classify Clifford algebras and describe their relation to Spin groups. Studying the irreducible representations of Clifford algebras we get interesting isomorphisms for low dimensional Spin groups. And, at the very end, with the machinery developed we study the construction of non-vanishing vector fields over the sphere and the projective space." -- Tomado del Formato de Documento de Grado.