Abstract
We characterize approximate biprojectivity of semigroup algebras related to a Clifford semigroup. As an application, we improve (Corollary 2.6 in Essmaili et al., Arch Math (Basel) 97(2):167–177, 2011) and we characterize pseudo-contractibility of the Clifford semigroup algebra. Namely, we show that \( \ell ^{1}(S) \) is pseudo-contractible if and only if the idempotent set E(S) is locally finite, each maximal subgroup \( G_{p} \) is finite for every \( p\in E(S) \), and \( \ell ^{1}(S) \) has a central approximate identity.
This is a preview of subscription content, log in via an institution to check access.
References
Askari-Sayah, M., Pourabbas, A., Sahami, A.: Johnson pseudo-contractibility of certain semigroup algebras. II. Semigroup Forum 104(1), 18–27 (2022)
Choi, Y.: Biflatness of \(\ell ^1\)-semilattice algebras. Semigroup Forum 75(2), 253–271 (2007)
Dales, H.G., Lau, A.T.M., Strauss, D.: Banach algebras on semigroups and on their compactifications. Mem. Am. Math. Soc. 205(966), 165 (2010)
Duncan, J., Paterson, A.L.T.: Amenability for discrete convolution semigroup algebras. Math. Scand. 66(1), 141–146 (1990)
Essmaili, M., Rostami, M., Medghalchi, A.R.: Pseudo-contractibility and pseudo-amenability of semigroup algebras. Arch. Math. (Basel) 97(2), 167–177 (2011)
Ghahramani, F., Zhang, Y.: Pseudo-amenable and pseudo-contractible Banach algebras. Math. Proc. Camb. Philos. Soc. 142(1), 111–123 (2007)
Ghandehari, M., Hatami, H., Spronk, N.: Amenability constants for semilattice algebras. Semigroup Forum 79(2), 279–297 (2009)
Howie, J.M.: Fundamentals of Semigroup Theory. London Mathematical Society Monographs. New Series, vol. 12. Clarendon Press, Oxford (1995)
Ramsden, P.: Biflatness of semigroup algebras. Semigroup Forum 79(3), 515–530 (2009)
Runde, V.: Amenable Banach Algebras. A Panorama, Springer Monographs in Mathematics, Springer, New York (2020)
Sahami, A., Pourabbas, A.: Approximate biprojectivity of certain semigroup algebras. Semigroup Forum 92(2), 474–485 (2016)
Sahami, A., Pourabbas, A.: Approximate biprojectivity and \(\phi \)-biflatness of certain Banach algebras. Colloq. Math. 145, 273–284 (2016)
Zhang, Y.: Nilpotent ideals in a class of Banach algebras. Proc. Am. Math. Soc. 127(11), 3237–3242 (1999)
Acknowledgements
The authors wish to thank the anonymous referee for his/her careful reading of the manuscript and his/her useful suggestions and comments. The first author is thankful to Ilam university, for their support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Anthony To-Ming Lau.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sahami, A., Askari-Sayah, M., Shariati, S.F. et al. A note on approximate biprojectivity of some semigroup algebras. Semigroup Forum 105, 570–574 (2022). https://doi.org/10.1007/s00233-022-10314-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00233-022-10314-1