Hochschild homology of structured algebras

TY - JOUR

T1 - Hochschild homology of structured algebras

AU - Wahl, Nathalie

AU - Westerland, Craig Christopher

PY - 2016/1/22

Y1 - 2016/1/22

N2 - We give a general method for constructing explicit and natural operations on the Hochschild complex of algebras over any prop with A∞-multiplication—we think of such algebras as A∞-algebras “with extra structure”. As applications, we obtain an integral version of the Costello–Kontsevich–Soibelman moduli space action on the Hochschild complex of open TCFTs, the Tradler–Zeinalian and Kaufmann actions of Sullivan diagrams on the Hochschild complex of strict Frobenius algebras, and give applications to string topology in characteristic zero. Our main tool is a generalization of the Hochschild complex.

AB - We give a general method for constructing explicit and natural operations on the Hochschild complex of algebras over any prop with A∞-multiplication—we think of such algebras as A∞-algebras “with extra structure”. As applications, we obtain an integral version of the Costello–Kontsevich–Soibelman moduli space action on the Hochschild complex of open TCFTs, the Tradler–Zeinalian and Kaufmann actions of Sullivan diagrams on the Hochschild complex of strict Frobenius algebras, and give applications to string topology in characteristic zero. Our main tool is a generalization of the Hochschild complex.

KW - math.AT

KW - math.QA

U2 - 10.1016/j.aim.2015.10.017

DO - 10.1016/j.aim.2015.10.017

M3 - Journal article

SN - 0001-8708

VL - 288

SP - 240

EP - 307

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -