Low dimensional modules over quantum complete intersections in two variables

doi:10.1007/s11464-019-0764-x

Front. Math. China

2019, Vol. 14

Issue (2) : 449-474 https://doi.org/10.1007/s11464-019-0764-x

RESEARCH ARTICLE

Low dimensional modules over quantum complete intersections in two variables

Hanyang YOU, Pu ZHANG(

)

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200241, China

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Abstract

We classify all the indecomposable modules of dimension≤5 over the quantum exterior algebra $k (x, y) / 〈 x 2, y 2, x y + q y x 〉$ in two variables, and all the indecomposable modules of dimension≤3 over the quantum complete intersection $k (x, y) / 〈 x m, y n, x y + q y x 〉$ in two variables, where m or n≥3, by giving explicitly their diagram presentations.

Keywords Quantum exterior algebra quantum complete intersection diagram presentation of a module

Corresponding Author(s): Pu ZHANG

Issue Date: 14 May 2019

Cite this article:

Hanyang YOU,Pu ZHANG. Low dimensional modules over quantum complete intersections in two variables[J]. Front. Math. China, 2019, 14(2): 449-474.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0764-x
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I2/449

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