Abstract
An(n−1)/2+1 parameter, solution of the Yang Baxter equation is presented giving rise to the quantum Group\(GL_{X;q_{ij} } (n)\). Determinant and inverse are constructed. The group acts covariantly on a quantum vector space of non-commutative coordinates. The associated exterior space can be identified with the differentials exhibiting a multiparameter deformed differential calculus following the construction of Wess and Zumino.
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References
J. Wess, B. Zumino: Covariant differential calculus on the quantum hyperplane.
Yu.I. Manin: Quantum groups and non-commutative geometry. Proc. Int. Congr. Math. 1, (1986) 798, Commun. Math. Phys. 123 (1989) 169
D.D. Demidov, Yu.I. Manin, E.E. Mukhin, D.V. Zhdanovich: Non-standard quantum deformations ofGL(n) and constant solutions of the Yang-Baxter equation, preprint Kyoto Univ. RIMS-701 (1990)
A. Sudbery: J. Phys. A. 23 (1990) 697
A. Schirrmacher, J. Wess, B. Zumino: Z. Phys. C — Particles and Fields 49 (1991) 317
E. Abe: Hopf Algebras. CUP (1977)
L.A. Takhtajan: Ad. Stud. Pure Math. 19 (1989)
M. Jimbo: Commun. Math. Phys. 102 (1986) 537
A. Sudbery: Matrix-element bialgebras determined by quadratic coordinate algebras, preprint, University of York (1990)
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Schirrmacher, A. The multiparametric deformation ofGL(n) and the covariant differential calculus on the quantum vector space. Z. Phys. C - Particles and Fields 50, 321–327 (1991). https://doi.org/10.1007/BF01474085
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DOI: https://doi.org/10.1007/BF01474085