On the construction of unitary quantum group differential calculus
Abstract
We develop a construction of the unitary type anti-involution for the quantized differential calculus over {{GL}}q(n) in the case | q| =1. To this end, we consider a joint associative algebra of quantized functions, differential forms and Lie derivatives over {{GL}}q(n)/{{SL}}q(n), which is bicovariant with respect to {{GL}}q(n)/{{SL}}q(n) coactions. We define a specific non-central spectral extension of this algebra by the spectral variables of three matrices of the algebra generators. In the spectrally expended algebra, we construct a three-parametric family of its inner automorphisms. These automorphisms are used for the construction of the unitary anti-involution for the (spectrally extended) calculus over {{GL}}q(n).
This work has been funded by the Russian Academic Excellence Project ‘5-100’. The results of section 5 (propositions 5.2, 5.3 and theorem 5.5) have been obtained under support of the RSF grant No.16-11-10160.- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- October 2016
- DOI:
- 10.1088/1751-8113/49/41/415202
- arXiv:
- arXiv:1504.04442
- Bibcode:
- 2016JPhA...49O5202P
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematical Physics;
- 58B32;
- 81R50
- E-Print:
- 26 pages, no figures