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The global dimension of ω-smash coproducts

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Abstract

We mainly study the global dimension of ω-smash coproducts. We show that if H is a Hopf algebra with a bijective antipode S H , and C ω ⋈ H denotes the ω-smash coproduct, then

gl.dim(C ω ⋈ H) ≤ gl.dim(C) + gl.dim(H),

where gl.dim(H) denotes the global dimension of H as a coalgebra.

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Authors and Affiliations

  1. Nanjing Agricultural University, Nanjing, China

    L. Y. Zhang & W. Pan

Authors
  1. L. Y. Zhang
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  2. W. Pan
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Correspondence to L. Y. Zhang.

Additional information

Published in Russian in Matematicheskie Zametki, 2013, Vol. 94, No. 4, pp. 541–551.

The text was submitted by the authors in English.

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Zhang, L.Y., Pan, W. The global dimension of ω-smash coproducts. Math Notes 94, 499–507 (2013). https://doi.org/10.1134/S0001434613090204

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  • DOI: https://doi.org/10.1134/S0001434613090204

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