First Order Differential Calculus on the Jordanian Twisted \(\star \)-Hopf Supersymmetry Algebra

IF 1.2 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-07-19 DOI:10.1007/s00006-025-01398-3

H. Fakhri, S. Laheghi

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Abstract

A Jordanian deformation of the \(N=2\) supersymmetry algebra and its first-order noncommutative differential calculus is obtained from the q-deformed Hopf supersymmetry algebra via a singular limit of a linear transformation. We show that the Jordanian \(N=2\) supersymmetry algebra carries a Hopf superalgebra structure. It is enhanced to a twisted Hopf star superalgebra by four inequivalent families of \(\star \)-structures. It is demonstrated that these star operations induce four types of \(\star \)-involutions on the differential one-forms and partial derivatives. We introduce an appropriate Jordanian super-Hopf algebra that includes two even and two odd generators equipped with four different types of \(\star \)-structures and its corresponding supergroup on the Hopf \(N=2\) supersymmetry algebra. It is shown that the noncommutative differential calculus over the Jordanian \(N=2\) supersymmetry algebra is left-covariant with respect to the Jordanian supergroup. The \(\star \)-structures of the supergroup are \(\star \)-preserving on the supersymmetry algebra only for zero values of their parameters.

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jordan扭曲\(\star \) -Hopf超对称代数的一阶微分

利用线性变换的奇异极限，从q变形的Hopf超对称代数得到\(N=2\)超对称代数的约旦变形及其一阶非交换微分。我们证明了Jordanian \(N=2\)超对称代数带有Hopf超代数结构。利用\(\star \) -结构的四个不等价族将其增强为一个扭曲Hopf星超代数。证明了这些星形运算在微分一型和偏导数上产生了四种\(\star \) -对合。在Hopf \(N=2\)超对称代数上，我们引入了一个合适的Jordanian超Hopf代数，它包括两个偶发生器和两个奇发生器，配备了四种不同类型的\(\star \) -结构及其对应的超群。证明了Jordanian \(N=2\)超对称代数上的非交换微分对于Jordanian超群是左协变的。超群的\(\star \) -结构在超对称代数上只有当其参数为零时才保持\(\star \) -不变。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.