Hopf algebra actions on differential graded algebras and applications
He, Ji-Wei ; Van Oystaeyen, Fred ; Zhang, Yinhuo
Bull. Belg. Math. Soc. Simon Stevin, Tome 18 (2011) no. 1, p. 99-111 / Harvested from Project Euclid
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Let $H$ be a finite dimensional semisimple Hopf algebra, $A$ a differential graded (dg for short) $H$-module algebra. Then the smash product algebra $A\#H$ is a dg algebra. For any dg $A\#H$-module $M$, there is a quasi-isomorphism of dg algebras: $\RHom_A(M,M)\#H\longrightarrow \RHom_{A\#H}(M\ot H,M\ot H)$. This result is applied to $d$-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras.
Publié le : 2011-03-15
Classification:  differential graded algebra,  smash product,  Yoneda algebra,  16E45,  16E40,  16W50 
@article{1299766491,
     author = {He, Ji-Wei and Van Oystaeyen, Fred and Zhang, Yinhuo},
     title = {Hopf algebra actions on differential graded algebras and applications},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {18},
     number = {1},
     year = {2011},
     pages = { 99-111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1299766491}
}

He, Ji-Wei; Van Oystaeyen, Fred; Zhang, Yinhuo. Hopf algebra actions on differential graded algebras and applications. Bull. Belg. Math. Soc. Simon Stevin, Tome 18 (2011) no. 1, pp.  99-111. http://gdmltest.u-ga.fr/item/1299766491/