Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weightspaces of dimension not exceeding two |
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Authors: | Christiane Martin Alain Piard |
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Institution: | (1) Physique Mathematique, U.A. CNRS 1102, University of Bourgogne, B.P. 138, F-21004 Dijon Cedex, France |
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Abstract: | In view of 1,2] any bounded admissible moduleA over the Virasoro Lie algebra is a finite length extension of irreducible modules with one-dimensional weightspaces. To each extension of finite lengthn are associatedn+1 invariants (a1,
1, ...,
n
). We prove that we have
i
–
j
{0, 1, ... 6(n – 1b)} for all (i, j) with 1ijn. In the casen=2 this result allows us to construct all the indecomposable bounded admissible modules, where the dimensions of the weightspaces are less than or equal to two. In particular we obtain all the extensions of two irreducible bounded-modules. |
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Keywords: | |
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