Ext^1-quivers for the Witt algebra W(1,1)

Details Ext^1-quivers for the Witt algebra W(1,1) Ext^1-quivers for the Witt algebra W(1,1)

2008-05-15

arxiv.org/abs/0805.2313v1

Mathematics

Representation Theory

16 pages, 2 figures

Scientific paper

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 \chi in g^*. Given such a \chi one can form the (finite dimensional) reduced enveloping algebra u(g,\chi). The simple modules for u(g,\chi) are precisely those simple W(1,1)-modules admitting the character \chi. In this paper the authors compute Ext^1 between pairs of simple modules for u(g,\chi).

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