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Derivations and automorphisms of the positive part of the two-parameter quantum group U r,s (B 3)

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Abstract

We compute the derivations of the positive part of the two-parameter quantum group U r,s (B 3) and show that the Hochschild cohomology group of degree 1 of this algebra is a three-dimensional vector space over the base field C. We also compute the groups of (Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra Ǔ r,s ≥0(B 3).

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Acknowledgements

We thank the referees for their time and comments. Xiu Ling Wang worked on this paper during her visit to University of California, Los Angeles, in 2015–2016. She would like to express her gratitude to host professor Igor Pak for his kind encouragement and help during her stay.

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Authors and Affiliations

  1. School of Sciences, Tianjin University of Science and Technology, Tianjin, 300222, P. R. China

    Min Li

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Xiu Ling Wang

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  1. Min Li
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  2. Xiu Ling Wang
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Correspondence to Xiu Ling Wang.

Additional information

The first author is supported by Specialized Research Fund for the Doctoral Program of Highter Education (Grant No. 20130031110005); the second author is supported by NSFC (Grant No. 11271131)

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Li, M., Wang, X.L. Derivations and automorphisms of the positive part of the two-parameter quantum group U r,s (B 3). Acta. Math. Sin.-English Ser. 33, 235–251 (2017). https://doi.org/10.1007/s10114-017-5787-1

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  • DOI: https://doi.org/10.1007/s10114-017-5787-1

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