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Quantum deformations of \(\text{GL}_ n\). (English) Zbl 0753.17015
The authors construct a family of deformations depending on \(1+{n \choose 2}\) parameters for the ring of functions on \(\text{GL}_ n\). First of all, they construct a family of Hopf algebras using the method of Yu. I. Manin, introduced in [Quantum groups and non-commutative geometry (Univ. Montreal, 1988; Zbl 0724.17006)]. Then they show that the algebras in the family are twists of the one-parameter family \({\mathcal O}(\text{GL}_ n(q))\) of deformations of the ring of functions on \(\text{GL}_ n\) by 2-cocycles.

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
20G42 Quantum groups (quantized function algebras) and their representations
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