Vol. 234, No. 1, 2008

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ISSN: 0030-8730
Category 𝒪 for the Virasoro algebra: cohomology and Koszulity

Brian D. Boe, Daniel K. Nakano and Emilie Wiesner

Vol. 234 (2008), No. 1, 1–21
Abstract

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
Mathematical Subject Classification 2000
Primary: 17B68, 17B10, 17B56, 17B65
Milestones
Received: 19 January 2007
Revised: 23 July 2007
Accepted: 1 August 2007
Published: 1 January 2008
Authors
Brian D. Boe
Department of Mathematics
University of Georgia
Athens, GA 30602
http://www.math.uga.edu/~brian/
Daniel K. Nakano
Department of Mathematics
University of Georgia
Athens, GA 30602
http://www.math.uga.edu/~nakano/
Emilie Wiesner
Mathematics Department
Williams Hall 212, Ithaca College
953 Danby Road
Ithaca, NY 14850
http://faculty.ithaca.edu/ewiesner/