Exceptional sequences and Drinfeld double Hall algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Ruan, Shiquan¹  Zhang, Haicheng² 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Inst Math, Nanjing 210023, Jiangsu, Peoples R China

关键词: Exceptional sequences;    Drinfeld double Hall algebras;    Mutation formulas;   

DOI  :  10.1016/j.jpaa.2019.05.006

来源: Elsevier

【 摘 要 】

Let A be a finitary hereditary abelian category and D(A) be its reduced Drinfeld double Hall algebra. By giving explicit formulas in D(A) for left and right mutations, we show that the subalgebras of D(A) generated by exceptional sequences are invariant under mutation equivalences. As an application, we obtain that if A is the category of finite dimensional modules over a finite dimensional hereditary algebra, or the category of coherent sheaves on a weighted projective line, the double composition algebra of A is generated by any complete exceptional sequence. Moreover, for the Lie algebra case, we also have paralleled results. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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