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

1995/09/29 by V. P. Akulov, Akulov, V. P., V. D. Gershun +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9509030

LaTeX, 22 pages

arxiv created 1995/09/29 · openalex publication_date 1995/09/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→ 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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