- #1
Monocles
- 466
- 2
I do not know if this is a common/standard construction, so here is my motivation for this question. From http://arxiv.org/abs/1002.1709" page 29:
Is there a word for when there is such a one-to-one correspondence?
Generally speaking, an ideal of an algebra defines a module. To see this, consider a vector [itex]|\mathcal{I} \rangle[/itex] which is annihilated by all elements of the ideal [itex]\mathcal{I}[/itex]. From [itex]|\mathcal{I}\rangle[/itex], we can generate a finite-dimensional representation of the algebra [itex]A[/itex] by acting with elements of [itex]A[/itex] on it. However, the converse is not always true. Fortunately, when modules are [itex]\hat{\theta}[/itex]-stable and invariant under the [itex]U(1)^2[/itex] symmetry, it was shown in Refs 33, 34 that there is a one-to-one correspondence between ideals and modules.
Is there a word for when there is such a one-to-one correspondence?
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