In the course, we consider Clifford algebras over the field of real or complex numbers. We discuss quaternions, Grassmann algebras, matrix representations of Clifford algebras, the Cartan-Bott 8-periodicity, Lipschitz groups and Clifford groups, the theorem on the two-sheeted covering of orthogonal groups by spin groups in the case of arbitrary dimension and signature of the space, the Cartan-Dieudonne theorem, unitary Lie groups in Clifford algebras, the Dirac equation, Pauli, Dirac, Weyl, Majorana, and Majorana-Weyl spinors, etc. Clifford algebra is a mathematical tool that is actively used in various branches of modern mathematics and physics – field theory, geometry, computer science, robotics, signal and image processing, etc.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Lecturer
Shirokov Dmitry Sergeevich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center