Hochschild homology and cohomology of down-up algebras

JOURNAL OF ALGEBRA

卷:498

Article

Chouhy, Sergio¹  Herscovich, Estanislao^1,2,3  Solotar, Andrea^1,3 

[1] UBA, CONICET Consejo Nacl Invest Cient & Tecn, IMAS, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

[2] Univ Grenoble Alpes, Inst Fourier, 100 Rue Maths, F-38610 Gieres, France

[3] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

关键词: Down-up algebra;    Homology;    Hochschild;    Resolution;   

DOI  :  10.1016/j.jalgebra.2017.11.026

来源: Elsevier

【 摘 要 】

We present a detailed computation of the cyclic and the Hochschild homology and cohomology of generic and 3-Calabi-Yau homogeneous down up algebras. This family was defined by Benkart and Roby in [3] in their study of differential posets. Our calculations are completely explicit, by making use of the Koszul bimodule resolution and some arguments similar to those used in [13] to compute the Hochschild cohomology of Yang Mills algebras. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free