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Derivations of the positive part of the two-parameter quantum group of type \(G_2\). (English) Zbl 1516.17019

The main result of the paper under review is the determination of the algebra of derivations of the positive part \(U^+_{r, s} (G_2)\) of the two-parameter quantized enveloping algebra \(U_{r, s} (G_2)\). This is achieved by embedding \(U^+_{r, s} (G_2)\) into a quantum torus with known derivations. As a consequence it is shown that the first Hochschild cohomology group of \(U^+_{r, s} (G_2)\) is a two-dimensional vector space over field of complex numbers.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B56 Cohomology of Lie (super)algebras
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