and Cl3,0(R) is algebra isomorphic via an R-linear map, Cl2(C) and Cl3,0(R) are R-algebra isomorphic. A table of this classification for follows. Here runs vertically and runs horizontally (e.g. the algebra is found in row 4, column −2). Symmetries There is a tangled web of symmetries and relationships in the above table. Going over 4 spots in any row yields an identical algebra. From these Bott periodicity follows: If the signature satisfies then (The table is symmetric about columns with signature ..., −7, −3, 1, 5, ...) Thus if the signature satisfies , See also Dirac algebra Cl1,3(C) Pauli algebra Cl3,0(R) Spacetime algebra Cl1,3(R) Clifford module Spin representation References Ring theory Clifford algebras Mathematical classification systems