Operations On Super Vector Spaces
The dual space V* of a super vector space V can be regarded as a super vector space by taking the even functionals to be those that vanish on V1 and the odd functionals to be those that vanish on V0. Equivalently, one can define V* to be the space of linear maps from V to K1|0 (the base field K thought of as a purely even super vector space) with the gradation given in the previous section.
Direct sums of super vector spaces are constructed as in the ungraded case with the grading given by
One can also construct tensor products of super vector spaces. Here the additive structure of Z2 comes into play. The underlying space is as in the ungraded case with the grading given by
where the indices are in Z2. Specifically, one has
Read more about this topic: Super Vector Space
Famous quotes containing the words operations and/or spaces:
“It may seem strange that any road through such a wilderness should be passable, even in winter, when the snow is three or four feet deep, but at that season, wherever lumbering operations are actively carried on, teams are continually passing on the single track, and it becomes as smooth almost as a railway.”
—Henry David Thoreau (1817–1862)
“Deep down, the US, with its space, its technological refinement, its bluff good conscience, even in those spaces which it opens up for simulation, is the only remaining primitive society.”
—Jean Baudrillard (b. 1929)