Scalar product for the tensor operators of the quantum algebra Ŭq(su2) by the Wigner–Eckart theorem

We present classical groups SL⋆(2) and SU⋆(2) as well as classical Lie algebra sl2⋆(C) associated with a new associative multiplication on 2 × 2 matrices. The idea of the new multiplication is generalized to the action of a 2 × 2 square matrix on a 2 × 1 column one. The coordinate Hopf algebra O(SLq⋆(2)) is introduced as a q-generalization of Hopf algebra O(SL⋆(2)), and it is shown that the coordinate algebra corresponding to the quantum plane Cq2 is a SLq⋆(2)-left-covariant algebra. Furthermore, the quantized universal enveloping algebra Uq(sl2⋆) with the Hopf structure as a dual of O(SLq⋆(2)) is introduced. For each of the Hopf algebras O(SLq⋆(2)) and Uq(sl2⋆), we associate two different real forms with two inequivalent families of *-involutions, with O(SUq⋆(2)) and Uq(su2⋆) as one of the real forms. It is shown that the Hopf algebra pairing is a dual pairing of two Hopf *-algebras O(SUq⋆(2)) and Uq(su2⋆).

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Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra

Fakhri

Laheghi

2021

Journal of Mathematical Physics

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We introduce a Hopf algebra structure on the N = 2 quantum supersymmetry algebra and formulate a first order quantum differential calculus on it. Then, it is enhanced to three *-calculi by defining three appropriate involution maps on the quantum super-algebra. Two of the *-structures correspond to quantum complex super-algebra and the other correspond to a quantum real one. An appropriate quantum super-Hopf algebra including two even and two odd generators and also its corresponding quantum super-group are introduced. Compared to the quantum super-algebra, the quantum super-group also has three different *-structures. It is shown that the differential calculus over the quantum super-algebra is left-covariant with respect to the quantum super-group. Besides, it is shown that the graded differential algebra for the case q = 1 is a bicovariant bimodule over the undeformed Hopf supersymmetry algebra.

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Scalar product for the tensor operators of the quantum algebra Ŭ_q(su₂) by the Wigner–Eckart theorem

Cited by 4 publications

References 9 publications

Right SUq(2)- and left SU
Fakhri
¹
,
Nouraddini
²

2016
Journal of Geometry and Physics
4
0
1
0
View full text Add to dashboard Cite

Right SUq(2)- and left SU
Fakhri
¹
,
Nouraddini
²

2016
Journal of Geometry and Physics
4
0
1
0
View full text Add to dashboard Cite

The quantum group SLq⋆(2) and quantum algebra Uq(sl2⋆) based on a new associative multiplication on 2 × 2 matrices

Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra

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Scalar product for the tensor operators of the quantum algebra Ŭq(su2) by the Wigner–Eckart theorem

Cited by 4 publications

References 9 publications

Right SUq(2)- and left SUFakhri1, Nouraddini2 2016Journal of Geometry and Physics4010View full textAdd to dashboardCite

Right SUq(2)- and left SUFakhri1, Nouraddini2 2016Journal of Geometry and Physics4010View full textAdd to dashboardCite

The quantum group SLq⋆(2) and quantum algebra Uq(sl2⋆) based on a new associative multiplication on 2 × 2 matrices

Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra

Contact Info

Product

Resources

About

Scalar product for the tensor operators of the quantum algebra Ŭ_q(su₂) by the Wigner–Eckart theorem

Right SUq(2)- and left SU
Fakhri
¹
,
Nouraddini
²

2016
Journal of Geometry and Physics
4
0
1
0
View full text Add to dashboard Cite

Right SUq(2)- and left SU
Fakhri
¹
,
Nouraddini
²

2016
Journal of Geometry and Physics
4
0
1
0
View full text Add to dashboard Cite