Еще одна задумка: статья про категорию O^ctr

[posic]

Название: The contra version of the category O

Аннотация: The semicoderived category of the category O over the Virasoro or Kac-Moody Lie algebra is equivalent to the semicontraderived category of the contra version of the category O with the complementary or shifted central charge. In this paper we show that the forgetful functor from the contra version of the category O into the category of modules over the Lie algebra is fully faithful. Similarly, the forgetful functor from the category of contramodules over the topological Lie algebra into the category of modules over the underlying discrete Lie algebra is fully faithful for Lie algebras such as the Virasoro and Kac-Moody. These assertions extend the line of known results claiming that the forgetful functors from contramodules to modules are fully faithful under certain assumptions.

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The semicoderived category of the category O over a Tate Lie algebra is equivalent to the semicontraderived category of the contra version of the category O with the complementary or shifted central charge. In a number of more elementary situations, including contramodules over a topological ring with the S-topology or the I-adic topology, or contramodules over a locally profinite group, it is already known or essentially known that the forgetful functor from the category of contramodules into the category of modules is fully faithful, under certain assumptions. We review and generalize this line of results in this paper. Then we proceed to show that the forgetful functor from the contra version of the category O into the category of modules over the Lie algebra is fully faithful for many Tate Lie algebras, such as the Virasoro or Kac-Moody. Similarly, the forgetful functor from the category of contramodules over the topological Lie algebra into the category of modules over the underlying discrete Lie algebra is fully faithful for such Lie algebras.