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Matched differential calculus on the quantum groups $GL_q(2,C),SL_q(2,C),C_q(2|0)$

V. P. Akulov·V. D. Gershun
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Abstract

We proposed the construction of the differential calculus on the quantum group and its subgroup with the property of the natural reduction: the differential calculus on the quantum group $GL_q(2,C)$ has to contain the differential calculus on the quantum subgroup $SL_q(2,C)$ and quantum plane $C_q(2|0)$ (''quantum matrjoshka''). We found, that there are two differential calculi, associated to the left differential Maurer--Cartan 1-forms and to the right differential 1-forms. Matched reduction take the degeneracy between the left and right differentials. The classical limit ($q\to 1$) of the ''left'' differential calculus and of the ''right'' differential calculus is undeformed differential calculus. The condition ${\cal D}_qG=1$ gives the differential calculus on $SL_q(2,C)$, which contains the differential calculus on the quantum plane $C_q(2|0)$.

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BibTeXRIS

V. P. Akulov, V. D. Gershun. 1995-09-29. Matched differential calculus on the quantum groups $GL_q(2,C),SL_q(2,C),C_q(2|0)$. https://arxiv.org/abs/q-alg/9509030

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