Any supernumber can be expressed uniquely in the form
1 Body and soul
The body of a supernumber is defined as , and its soul is defined as . If then has an inverse given by
2 Odd and even
A supernumber can be decomposed into the even and odd parts:
Even supernumbers commute with each other and are called c-numbers, while odd supernumbers anticommute with each other and are called a-numbers. Note, the product of two c-numbers is even, the product of a c-number and an a-number is odd, and the product of two a-numbers is even. The superalgebra has the vector space decomposition , where is the space of c-numbers, and is the space of a-numbers.
3 Conjugation and involution
The second way is to define an anti-linear involution:
The comes down to whether the product of two real odd supernumbers is real or imaginary.
|Date of creation||2013-03-22 13:03:27|
|Last modified on||2013-03-22 13:03:27|
|Last modified by||mhale (572)|