Abstract
The main purpose of this paper is to investigate the character amenability of semigroup algebras. In this regard, the new concept character amenability modulo an ideal of Banach algebras are introduced. For a large class of semigroups such as E-inversive E-semigroup and eventually inverse semigroups, it is shown that the semigroup S is amenable if and only if the semigroup algebra \(l^1(S)\) is character amenable modulo an ideal. Some characterizations of character amenability modulo an ideal of Banach algebras are studied and interesting examples are presented.
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References
Duncan, J., Namioka, I.: Amenability of inverse semigroups and their semigroup algebras. Proc. R. Soc. Edinburgh Sect. A 80, 309–321 (1978)
Dales, G.K., Lau, A.T.-M., Strauss, D.: Banach algebras on semigroups and their compactifications, Memoirs American Mathematical Society, Vol. 205, No. 966. Providence (2010)
Sangani Monfared, M.: Character amenability of Banach algebras. Math. Proc. Camb. Philos. Soc. 144, 697–706 (2008)
Kaniuth, E., Lau, A.T., Pym, J.: On \(\varphi \)-Amenability of Banach algebras. Math. Proc. Camb. Phil. Soc. 144, 85–96 (2008)
Johnson, B.E.: Cohomology in Banach algebras, Memoirs Amer. Math. Soc. 127 (1972)
Amini, M., Rahimi, H.: Amenability of semigroups and their algebras modulo a group congruence. Acta Mathematica Hungarica 144(2), 407–415 (2014)
Ghaffari, A.: On character amenability of semigroup algebras. Acta Math. Hungar. 134(1–2), 177–192 (2012)
Mewomo, O.T.: Various notions of amenability in Banach algebras. Expo. Math. 29, 283–299 (2011)
Maepa, S.M., Mewomo, O.T.: On character amenability of semigroup algebras. Quaestiones Mathematicae. 39(3), 1–12 (2015)
Gigon, R.S.: Congruences and group congruences on a semigroup. Semigroup Forum 86, 431–450 (2013)
Edwards, P.M.: Group congruences on arbitrary semigroups. Int. J. Algebra 6, 531–537 (2012)
Siripitukdet, M., Sattayaporn, S.: The least group congruence on E-inversive semigroups and E-inversive E-semigroups. Thai J. Math. 3, 163–169 (2005)
Runde, V.: Lectures on amenability. Lecture notes in mathematics, 1774, Springer (2002)
Clifford, A.H., Preston, J.B.: The Algebraic Theory of Semigroups I, American Mathematical Society Surveys 7. American Mathematical Society, Providence (1961)
Howie, J.M.: Fundamentals of semigroup theory. Clarendon Press, Oxford (1995)
Gomes, G.M.S.: Group congruences on eventually inverse semigroups. Portugaliae Mathematica 49(4), 417–428 (1992)
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Gholami, R., Rahimi, H. On character amenability of semigroup algebras. Boll Unione Mat Ital 12, 517–524 (2019). https://doi.org/10.1007/s40574-018-00189-y
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DOI: https://doi.org/10.1007/s40574-018-00189-y