Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 449–474 | Cite as

Low dimensional modules over quantum complete intersections in two variables

  • Hanyang You
  • Pu ZhangEmail author
Research Article


We classify all the indecomposable modules of dimension ⩽ 5 over the quantum exterior algebra kx, y〉/〈x2, y2, xy + qyx〉 in two variables, and all the indecomposable modules of dimension ⩽ 3 over the quantum complete intersection kx, y〉/〈xm, yn, xy + qyx〉 in two variables, where m or n ⩾ 3; by giving explicitly their diagram presentations.


Quantum exterior algebra quantum complete intersection diagram presentation of a module 


16G10 15A75 16G60 


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The authors sincerely thank the referees for carefully reading the manuscript and valuable suggestions


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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina

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