The first Hochschild (co)homology when adding arrows to a bound quiver algebra

JOURNAL OF ALGEBRA

卷:540

Article

Cibils, Claude¹  Lanzilotta, Marcelo²  Marcos, Eduardo N.³  Schroll, Sibylle⁴  Solotar, Andrea^5,6 

[1] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CNRS, Montpellier, France

[2] Univ Republica, Fac Ingn, Inst Matemat & Estadist Rafael Laguardia, Montevideo, Uruguay

[3] Univ Sao Paulo, Dept Matemat, IME, Sao Paulo, Brazil

[4] Univ Leicester, Dept Math, Leicester, Leics, England

[5] Univ Buenos Aires, Fac Ciencias Exactas & Nat, IMAS CONICET, Buenos Aires, DF, Argentina

[6] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Buenos Aires, DF, Argentina

关键词: Hochschild;    Cohomology;    Homology;    Relative;    Quiver;    Arrow;   

DOI  :  10.1016/j.jalgebra.2019.08.029

来源: Elsevier

【 摘 要 】

We provide a formula for the change of the dimension of the first Hochschild cohomology vector space of bound quiver algebras when adding new arrows. For this purpose we show that there exists a short exact sequence which relates the first cohomology vector spaces of the algebras to the first relative cohomology. Moreover, we show that the first Hochschild homologies are isomorphic when adding new arrows. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free