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## On the construction of unitary quantum group differential calculus

Journal of Physics A: Mathematical and Theoretical. 2016. Vol. 49. No. 41. P. 415202-(25pp).

We develop a construction of the unitary type anti-involution for the quantized differential calculus over GLq (n) in the case ∣q∣ = 1. To this end, we consider a joint associative algebra of quantized functions, differential forms and Lie derivatives over GLq (n)/SLq (n), which is bicovariant with respect to GLq (n)/SLq (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 GLq (n).