Complexity of modules over classical Lie superalgebras
| Autor: | Turkey, Houssein El |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of Algebra, Volume 445, Pages 365-393, 2016 |
| Druh dokumentu: | Working Paper |
| Popis: | The complexity of the simple and the Kac modules over the general linear Lie superalgebra $\mathfrak{gl}(m|n)$ of type $A$ was computed by Boe, Kujawa, and Nakano in 2012. A natural continuation to their work is computing the complexity of the same family of modules over the ortho-symplectic Lie superalgebra $\mathfrak{osp}(2|2n)$ of type $C$. The two Lie superalgebras are both of Type I which will result in similar computations. In fact, our geometric interpretation of the complexity agrees with theirs. We also compute a categorical invariant, z-complexity, introduced in Boe et al., and we interpret this invariant geometrically in terms of a specific detecting subsuperalgebra. In addition, we compute the complexity and the z-complexity of the simple modules over the Type II Lie superalgebras $\mathfrak{osp}(3|2)$, $D(2,1;\alpha)$, $G(3)$, and $F(4)$. Comment: arXiv admin note: text overlap with arXiv:1107.2579, arXiv:0905.2403 by other authors |
| Databáze: | arXiv |
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