Indecomposable representations of special linear Lie superalgebras. (English) Zbl 0933.17010
A classification of the finite dimensional indecomposable representations of the Lie superalgebra \(\text{sl}(m/1)\) is given. This is simplified since for \(\text{sl}(m/1)\) Kac modules either have length 1 (when they are typical), or length 2 (when they are atypical) [see J. Van der Jeugt, J. W. B. Hughes, R. C. King and J. Thierry-Mieg, Commun. Algebra 18, 3453-3480 (1990; Zbl 0721.17003) and V. Serganova, Sel. Math. 2, 607-651 (1996; Zbl 0881.17005)].
The classification of indecomposable representations is then obtained by the help of quivers (or directed graphs), and extended to blocks of simple modules. The author uses notions and arguments of category theory in his proofs. From here, he also gets the existence of wild representation type blocks when both \(m\) and \(n\) are \(\geq 2\).
A summary of his results were published earlier, in [C. R. Acad. Sci., Paris, Sér. I 324, No. 11, 1221-1226 (1997; Zbl 0885.17021)].
The classification of indecomposable representations is then obtained by the help of quivers (or directed graphs), and extended to blocks of simple modules. The author uses notions and arguments of category theory in his proofs. From here, he also gets the existence of wild representation type blocks when both \(m\) and \(n\) are \(\geq 2\).
A summary of his results were published earlier, in [C. R. Acad. Sci., Paris, Sér. I 324, No. 11, 1221-1226 (1997; Zbl 0885.17021)].
Reviewer: J.Van der Jeugt (Gent)
MSC:
| 17B70 | Graded Lie (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
References:
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