A Cacti theoretical interpretation of the axioms of bialgebras and H-module algebras

JOURNAL OF ALGEBRA

卷:427

Article

关键词: Cacti operad;    Bialgebras;    Module algebras;    Hochschild cohomology;    Gerstenhaber algebras;   

DOI  :  10.1016/j.jalgebra.2014.12.015

来源: Elsevier

【 摘 要 】

We establish a dictionary between the Cacti algebra axioms on a Cacti algebra structure with underlying free associative algebra, under suitable good behavior with degrees. Using these ideas, for an associative algebra A and a bialgebra H, we also translate Cacti algebra maps Omega(H) -> C-center dot(A) (where Omega(H) stands for the cobar construction on H and C-center dot(A) is the Hochschild cohomology complex) with H-module algebra structures on A, and illustrate with examples of applications. (c) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free