The Global Dimension of $\omega$-Smash Coproducts

L. Yu. Zhang, W. Pan

Nanjing Agricultural University

Abstract: 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, global dimension, $\omega$-smash coproduct.

UDC: 512.552

Received: 28.01.2012

DOI: 10.4213/mzm10321

 English version: Mathematical Notes, 2013, 94:4, 499–507

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