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Homological dimensions of smooth crossed products

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Abstract

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products \(\mathscr {S}(G, A; \alpha )\) for \(G = \mathbb {R}\) and \(G = \mathbb {T}\) and a self-induced Fréchet–Arens–Michael algebra A. To do this, we provide a powerful generalization of methods which are used in the works of Ogneva and Helemskii.

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Acknowledgements

I would like to thank Alexei Pirkovskii and Alexander Helemskii for encouraging me to work on this problem, and I greatly appreciate their feedback.

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Authors and Affiliations

  1. Department of Mathematics, Higher School of Economics, Usacheva str. 6, 119048, Moscow, Russia

    Petr Kosenko

  2. Department of Mathematics, University of Toronto, 40 St. George St., Toronto, ON, M5S 1A1, Canada

    Petr Kosenko

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  1. Petr Kosenko
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Correspondence to Petr Kosenko.

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Communicated by Zinaida Lykova.

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Kosenko, P. Homological dimensions of smooth crossed products. Ann. Funct. Anal. 12, 39 (2021). https://doi.org/10.1007/s43034-021-00125-w

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  • DOI: https://doi.org/10.1007/s43034-021-00125-w

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