期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1990
卷号：87
期号：2
页码：653-657
DOI：10.1073/pnas.87.2.653
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：A generalization is given of the notion of a symmetric bilinear form over a vector space, which includes variables of positive and negative signature ("supersymmetric variables"). It is shown that this structure is substantially isomorphic to the exterior algebra of a vector space. A supersymmetric extension of the second fundamental theorem of invariant theory is obtained as a corollary. The main technique is a supersymmetric extension of the standard basis theorem. As a byproduct, it is shown that supersymmetric Hilbert space and supersymplectic space are in natural duality.
