Category $\mathcal O$ for the Virasoro algebra: Cohomology and Koszulity

Details Category $\mathcal O$ for the Virasoro algebra: Cohomology and Koszulity Category $\mathcal O$ for the Virasoro algebra: Cohomology and Koszulity

2007-01-23

arxiv.org/abs/math/0701644v3

Brian D. Boe, Daniel K. Nakano, and Emilie Wiesner, Category $\mathcal O$ for the Virasoro algebra: Cohomology and Koszulity,

Mathematics

Representation Theory

17 pages, 5 EPS figures; v2: minor changes, final published version; v3: corrected author addresses

Scientific paper

We investigate blocks of the Category $\mathcal O$ for the Virasoro algebra over the complex numbers. We demonstrate that the blocks have Kazhdan-Lusztig theories, and that the truncated blocks give rise to interesting Koszul algebras. The simple modules have BGG resolutions, and from this we compute the extensions between Verma modules and simple modules, and between pairs of simple modules.

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