Geodesic
The Global Dimension of $\omega$-Smash Coproducts
Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 541-551

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We mainly study the global dimension of $\omega$-smash coproducts. We show that if $H$ is a Hopf algebra with a bijective antipode $S_H$, and $C{_\omega}\bowtie H$ denotes the $\omega$-smash coproduct, then $$ \mathrm{gl}.\mathrm{dim}(C_\omega\bowtie H)\leq \mathrm{gl}.\mathrm{dim}(C)+\mathrm{gl}.\mathrm{dim}(H), $$ where $\mathrm{gl}.\mathrm{dim}(H)$ denotes the global dimension of $H$ as a coalgebra.
Keywords: spectral sequence, $\omega$-smash coproduct.
Mots-clés : global dimension 
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     author = {L. Yu. Zhang and W. Pan},
     title = {The {Global} {Dimension} of $\omega${-Smash} {Coproducts}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a4/}
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L. Yu. Zhang; W. Pan. The Global Dimension of $\omega$-Smash Coproducts. Matematičeskie zametki, Tome 94 (2013) no. 4, pp. 541-551. http://geodesic.mathdoc.fr/item/MZM_2013_94_4_a4/