On simple mixed modules over the Virasoro algebra

V.S.Mazorchuk

We describe the support of a simple weight module over the Virasoro Lie algebra and classify all those modules, whose support is one element less than the weight lattice. Using the ideas from the proof of the latter result we derive some properties of the so-called mixed modules, that is the modules which have both finite-dimensional and infinite-dimensional weight spaces.

1. Martin C., Piard A. Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac, Comm. Math. Phys. 137 (1991), no. 1, 109--132.

2. Martin C., Piard A. Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weight spaces of dimension not exceeding two, Comm. Math. Phys. 150 (1992), no. 3, 465--493.

3. Mathieu O. Classification of Harish-Chandra modules over the Virasoro Lie algebra, Invent. Math. 107 (1992), no. 2, 225--234.

4. Mazorchuk V. Futorny theorem for generalized Witt algebras of rank $2$, Comm. Algebra 25 (1997), no. 2, 533--541.

5. Mazorchuk V. Classification of simple Harish-Chandra modules over $\mathbb{Q}$-Virasoro algebra, Math. Nachr. 209 (2000), 171--177.

6. Xu X. Pointed representations of Virasoro algebra. A Chinese summary appears in Acta Math. Sinica 40 (1997), no. 3, 479. Acta Math. Sinica (N.S.) 13 (1997), no. 2, 161--168.

7. Zhang H. A class of representations over the Virasoro algebra, J. Algebra 190 (1997), no. 1, 1--10.

	On simple mixed modules over the Virasoro algebra
Author	V.S.Mazorchuk mazor@math.uu.se Department of Mathematics, Uppsala University, Box 480, SE-75106, Uppsala, Sweden,
Abstract	We describe the support of a simple weight module over the Virasoro Lie algebra and classify all those modules, whose support is one element less than the weight lattice. Using the ideas from the proof of the latter result we derive some properties of the so-called mixed modules, that is the modules which have both finite-dimensional and infinite-dimensional weight spaces.
Keywords	simple mixed module, support, Virasoro Lie algebra
DOI	doi:10.30970/ms.22.2.121-128
Reference	1. Martin C., Piard A. Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac, Comm. Math. Phys. 137 (1991), no. 1, 109--132. 2. Martin C., Piard A. Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weight spaces of dimension not exceeding two, Comm. Math. Phys. 150 (1992), no. 3, 465--493. 3. Mathieu O. Classification of Harish-Chandra modules over the Virasoro Lie algebra, Invent. Math. 107 (1992), no. 2, 225--234. 4. Mazorchuk V. Futorny theorem for generalized Witt algebras of rank $2$, Comm. Algebra 25 (1997), no. 2, 533--541. 5. Mazorchuk V. Classification of simple Harish-Chandra modules over $\mathbb{Q}$-Virasoro algebra, Math. Nachr. 209 (2000), 171--177. 6. Xu X. Pointed representations of Virasoro algebra. A Chinese summary appears in Acta Math. Sinica 40 (1997), no. 3, 479. Acta Math. Sinica (N.S.) 13 (1997), no. 2, 161--168. 7. Zhang H. A class of representations over the Virasoro algebra, J. Algebra 190 (1997), no. 1, 1--10.
Pages	121-128
Volume	22
Issue	2
Year	2004
Journal	Matematychni Studii
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