Ext¹-quivers for the Witt algebra W(1,1)

2008/05/15 by Brian D. Boe, Boe, Brian D., Daniel K. Nakano +3
Mathematics · #17B55 (Primary) #17B68 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B55 #msc:17B68

paper · pdf · doi:10.48550/arxiv.0805.2313

16 pages, 2 figures

arxiv created 2008/05/15 · openalex publication_date 2008/05/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let g be the finite dimensional Witt algebra W(1,1) over an algebraically closed field of characteristic p > 3. It is well known that all simple W(1,1)-modules are finite dimensional. Each simple module admits a character χin g^*. Given such a χone can form the (finite dimensional) reduced enveloping algebra u(g,χ). The simple modules for u(g,χ) are precisely those simple W(1,1)-modules admitting the character χ. In this paper the authors compute Ext¹ between pairs of simple modules for u(g,χ).

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