Module contractibility for semigroup algebras
الموضوعات :
Abasalt Bodaghi
1
(Department of Mathematics, Islamic Azad University, Garmsar Branch,
Garmsar, Iran.)
الکلمات المفتاحية: Banach module, module contractibleity, module derivation, inverse semi-groups,
ملخص المقالة :
In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1(S)×l1(E)l1(S) is l1(E)-module contractible.
[1] M. Amini, Module amenability for semigroup algebras, Semigroup Forum,
69 (2004), 243{254.
[2] M. Amini, A. Bodaghi and D. Ebrahimi Bagha, Module amenability of
the second dual and module topological center of semigroup algebras,
Semigroup Forum, 80 (2010), 302{312.
[3] A. Bodaghi, Module amenability and tensor product of semigroup
algebras, J. Math. Extension, 4 (2010), 97{106.
[4] A. Bodaghi, The structure of module contractible Banach algebras, Int.
J. Nonlinear Anal., 1 (2010), 6{11.
[5] A. Bodaghi, Module amenability of the projective module tensor product,
Malaysian J. Math. Sci., 5 (2011), 257{265.
[6] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford
University Press, Oxford, 2000.
[7] J. Duncan, I. Namioka, Amenability of inverse semigroups and their
semigroup algebras, Proc. Roy. Soc. Edinburgh, 80 (1988), 309-321.
[8] G. H. Esslamzadeh and T. Esslamzadeh, Contractability of `1-Munn
Algebras with Applications, Semigroup Forum, 63 (2001), 1{10.
[9] N. Grnbk, Amenability of weighted discrete convolution algebras on
cancellative semigroups, Proc. Roy. Soc. Edinburgh, 110 (1998), 351{360.
[10] B. E. Johnson, Cohomology in Banach algebras, Memoirs Amer. Math.
Soc. 127, Amer. Math. Soc., Providence, 1972.
[11] W.D. Munn, A class of irreducible matrix representations of an arbitrary
inverse semigroup, Proc. Glasgow Math. Assoc., 5 (1961), 41{48.
[12] H. Pourmahmood-Aghababa, (Super) module amenability, module
topological centre and semigroup algebras, Semigroup Forum, 81 (2010),
344{356.
[13] H. Pourmahmood-Aghababa, A note on two equivalence relations on
inverse semigroups, Semigroup Forum, DOI 10.1007/s00233-011-
9365-z.
[14] R. Rezavand, M. Amini, M. H. Sattari, and D. Ebrahimi Bagha, Module
Arens regularity for semigroup algebras, Semigroup Forum, 77 (2008),
300{305.
[15] V. Runde, Lectures on Amenability, Lecture Notes in Mathematics 1774,
Springer-Verlag, Berlin-Heidelberg-New York, 2002.
[16] Yu. V. Selivanov, Banach algebras of small global dimension zero, Uspekhi
Mat. Nauk., 31 (1976), 227{228.