Algebr Represent Theor https://doi.org/10.1007/s10468-018-9803-7 Tensor Representations of q(∞) 1 2 D. Grantcharov · V. Serganova Received: 27 August 2017 / Accepted: 17 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract We introduce a symmetric monoidal category of modules over the direct limit queer superalgebra q(∞). This category can be defined in two equivalent ways with the aid of the large annihilator condition. Tensor products of copies of the natural and the conatural representations are injective objects in this category. We obtain the socle filtrations and formulas for the tensor products of the indecomposable injectives. In addition, it is proven that the category is Koszul self-dual. Keywords Queer superalgebras · Tensor representations · Koszul duality Mathematics Subject Classification (2010) 17B65 · 17B10 · 16G10 1 Introduction Recently new symmetric monoidal categories have attracted considerable attention. Among them are the categories Trep g of modules over direct limit g of classical Lie algebras gen- erated as abelian tensor categories by the natural and conatural representations. Namely, g is one of the following: gl(∞) = lim gl(n), o(∞) = lim o(n) and sp(∞) = lim sp(n). −→ −→ −→ In  it is proven that these categories
Algebras and Representation Theory – Springer Journals
Published: May 30, 2018
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