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Category 𝒪 for the Virasoro algebra: cohomology and
Koszulity
Brian D. Boe, Daniel K. Nakano and Emilie Wiesner |
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Vol. 234 (2008), No. 1, 1–21
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Abstract |
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We investigate blocks of the Category 𝒪 for the Virasoro algebra over ℂ. 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. |
Keywords
Virasoro algebra, Lie algebra cohomology, extensions
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Mathematical Subject Classification 2000
Primary: 17B68, 17B10, 17B56, 17B65
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Milestones
Received: 19 January 2007
Revised: 23 July 2007
Accepted: 1 August 2007
Published: 1 January 2008
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Authors |
| Brian D. Boe | |
| Department of Mathematics University of Georgia Athens, GA 30602 |
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| http://www.math.uga.edu/~brian/ | |
| Daniel K. Nakano | |
| Department of Mathematics University of Georgia Athens, GA 30602 |
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| http://www.math.uga.edu/~nakano/ | |
| Emilie Wiesner | |
| Mathematics Department Williams Hall 212, Ithaca College 953 Danby Road Ithaca, NY 14850 |
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| http://faculty.ithaca.edu/ewiesner/ | |
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