Complexity of modules over classical Lie superalgebras

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• 作者：Houssein El Turkey ^{helturkey@newhaven.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lie superalgebra ; Complexity of modules ; z-Complexity ; Support varieties ; Associated varieties
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：445
• 期：Complete
• 页码：365-393
• 全文大小：530 K

文摘

The complexity of the simple and the Kac modules over the general linear Lie superalgebra gl(m|n)$\mathfrak{gl}(m|n)$ of type A was computed by Boe, Kujawa, and Nakano in [2]. A natural continuation to their work is computing the complexity of the same family of modules over the ortho-symplectic Lie superalgebra osp(2|2n)$\mathfrak{osp}(2|2n)$ 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 [2], 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 osp(3|2)$\mathfrak{osp}(3|2)$, D(2,1;α)$D(2,1;\alpha )$, G(3)$G(3)$, and ccdf99b2" title="Click to view the MathML source">F(4)$F(4)$.