Abstract
In this work, we present a definition of an inverse semigroup, Pr(S), which is associated to an inverse semigroup S. Also, we show the existence of a kind of correspondence between partial representations of S and representations of Pr(S) on a Hilbert space. Some results of graded C *-algebras over a group are extended to pre-grading C *-algebras over inverse semigroups.
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References
Birget JC, Rhodes J (1984) Almost finite expansions of arbitrary semigroups. J Pure Appl Algebra 32(3):239–287
Buss A, Exel R, (2014) Inverse semigroup expansions and their actions on C *-algebras. J Ill Math 56:1185–1212
Exel R (1998) Partial actions of groups and actions of inverse semigroups. Proc Am Math Soc 126:3481–3494
Exel R (2008) Inverse semigroups and combinatorial C *-algebras. Bull Braz Math Soc.(N.S.) 39(2):191–313
Exel R, Laca M, Quigg J (2002) Partial dynamical systems and C *-algebras generated by partial isometries. J Oper Theory 47:169–186
Jensen K, Thomsen K (1991) Elements of KK-theory. Birkhauser, Boston
Lawson MV (1998) Inverse semigroups, the theory of partial symmetries. World Scientific Publishing Co., River Edge
Lawson MV, SMargolis SW, Steinberg B (2006) Expansions of inverse semigroups. J Aust Math Soc 80:205–228
Sieben N (1997) C *-Crossed products by partial actions and actions of inverse semigroups. J Aust Math Soc (Series A) 63:32–46
Tabatabaie Shourijeh B (2006) Partial inverse semigroup C *-algebra. Taiwan J Math 10(6):1539–1548
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The author would like to thank the referee for his (her) carefully reading of the manuscript.
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Tabatabaie Shourijeh, B. Representations of Inverse Semigroups and Pre-grading C *-Algebra. Iran J Sci Technol Trans Sci 40, 219–224 (2016). https://doi.org/10.1007/s40995-016-0097-5
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DOI: https://doi.org/10.1007/s40995-016-0097-5