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标题：On the uniqueness of the <mml:math alttext="$(2,2)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>-dimensional supertorus associated to a nontrivial representation of its underlying <mml:math alttext="$2$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn></mml:math>-torus, and having nontrivial odd brackets
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作者：R. Peniche ; O. A. Sánchez-Valenzuela ; F. Thompson 等
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204305107
出版社：Hindawi Publishing Corporation
摘要：It is proved that up to isomorphism there is only one (2,2)-dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and that it has nontrivial odd brackets. This supertorus is obtained by finding out first a canonical form for its Lie superalgebra, and then using Lie's technique to represent it faithfully as supervector fields on a supermanifold. Those supervector fields can be integrated, and through their various integral flows the composition law for the supergroup is straightforwardly deduced. It turns out that this supertorus is precisely the supergroup described by Guhr (1993) following a formal analogy with the classical unitary group U(2) but with no further intrinsic characterization.