Z_2^n grading of the classical Lie algebras

Abstract

The Z_2^n gradings of the classical Lie algebras are described. To elucidate the grading, the classical Lie algebras are expressed in terms of matrix algebras over one of eight fields or Clifford algebras which carry gradings ranging from zero to Z_2^3. When the matrix dimension is divisible by a power of two, the Lie algebras have higher gradings which may be expressed in terms of higher Clifford algebras: these are also described.