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Derivations of the Positive Part of the Two-parameter Quantum Group of Type G2

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Abstract

In this paper, we compute the derivations of the positive part of the two-parameter quantum group of type G2 by embedding it into a quantum torus. We also show that the first Hochschild cohomology group of this algebra is a two-dimensional vector space over the complex field.

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Acknowledgements

We would like to express our sincere thanks to the anonymous referees for their careful reading and valuable comments towards the improvement of this article.

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Authors and Affiliations

  1. School of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, P. R. China

    Yong Yue Zhong

  2. School of Mathematical Sciences, Heilongjiang University, Harbin, 150080, P. R. China

    Xiao Min Tang

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  1. Yong Yue Zhong
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  2. Xiao Min Tang
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Correspondence to Xiao Min Tang.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11771069) and Natural Science Foundation of Heilongjiang Province (Grant No. LH2020A020)

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Zhong, Y.Y., Tang, X.M. Derivations of the Positive Part of the Two-parameter Quantum Group of Type G2. Acta. Math. Sin.-English Ser. 37, 1471–1484 (2021). https://doi.org/10.1007/s10114-021-9571-x

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