The Jordan superalgebra JF(6/4) is the unique exceptional Jordan superalgebra that has no realization in terms of Z2-graded associative supermatrices. It is proposed to be the basis of an exceptional superspace that is non-Clifford algebraic. The JF(6/4) is constructed in a basis that renders itself to such an interpretation and its derivation, reduced structure, and Möbius superalgebras are studied. These algebras are simply the Lie superalgebras of generalized rotation, the Lorentz group, and conformal supergroup of the Jordan superalgebra JF(6/4). We also comment on the implications of the exceptionality of JF(6/4).
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics