张量代数的超扩张及其应用
Super-extensions of tensor algebras and their applications
AI总结：
本文在已有研究基础上构造两类张量代数超扩张，研究相关导子与算子生成空间的对偶定理，为Schur-Sergeev对偶及其量子版本提供新证明。
摘要：
在arXiv:0909.5586与arXiv:1411.4125的研究基础上，我们分别通过对称群与Hecke代数的超作用构造了普通张量代数的两类超扩张。对每类扩张，我们考察了一类源自余向量的特殊导子，研究了由这类导子、向量左乘算子与置换算子以特定方式生成的空间，证明了这类空间与超作用的对偶定理。作为应用，我们给出了Schur-Sergeev对偶定理及其量子版本的新证明。
英文摘要：
Following arXiv:0909.5586 and arXiv:1411.4125, we construct two super-extensions of the usual tensor algebra through the super-actions of symmetric groups and Hecke algebras respectively. For each extension, we consider a special type of derivations coming from covectors, and study the the space generated, in some special manner, by these derivations and operators from left multiplication by vectors and permutations. Duality theorems of these spaces and the super-actions are proved. As an application, we provide a new proof of the Schur-Sergeev duality theorem, as well as its quantum version.
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