General I-graded Vector Spaces
The subspaces of a graded vector space need not be indexed by the set of natural numbers, and may be indexed by the elements of any set I. An I-graded vector space V is a vector space that can be written as a direct sum of subspaces indexed by elements i of set I:
Therefore, an -graded vector space, as defined above, is just an I-graded vector space where the set I is (the set of natural numbers).
The case where I is the ring (the elements 0 and 1) is particularly important in physics. A -graded vector space is also known as a supervector space.
Read more about this topic: Graded Vector Space
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