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
Famous quotes containing the words general and/or spaces:
“A point has been reached where the peoples of the Americas must take cognizance of growing ill-will, of marked trends toward aggression, of increasing armaments, of shortening tempers—a situation which has in it many of the elements that lead to the tragedy of general war.... Peace is threatened by those who seek selfish power.”
—Franklin D. Roosevelt (1882–1945)
“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)