On Generalized Degenerate Lipschitz and Spin Groups
Ekaterina Filimoshina -- HSE University
In this talk, we introduce and study generalized Lipschitz and spin groups in degenerate geometric (Clifford) algebras of arbitrary dimension and signature. The generalized degenerate Lipschitz and spin groups contain the corresponding ordinary Lipschitz and spin groups as subgroups and coincide with them in the low-dimensional cases. We prove that an element of the generalized degenerate Lipschitz group can be represented as a product of an element of fixed parity and an element of the Grassmann subalgebra. It is shown that the values of norm functions of elements of the generalized degenerate Lipschitz groups belong to the kernel of the twisted adjoint representation. The introduced groups can be interesting for applications in physics, engineering, and computer science.