Spectra in Some Inverse Semigroup Algebras

M. J. Crabb, J. Duncan, C. M. McGregor
2004 Mathematical Proceedings of the Royal Irish Academy  
Let S be the semigroup with generators s j ; s j 1 (j 01; 2; . . . ; N) and defining relations s j 1s j 01; s j 1s k 0u (j "k); where 1 is the identity and u the zero. We determine the spectrum of the average of these generators in l 1 (S)=Cu; showing it to be an ellipse together with its interior. The major and minor diameters of the ellipse are 1'/1/N and 1 (/1/N, respectively. So the interior is non-empty except in the degenerate case N 0/1.
doi:10.3318/pria.2004.104.2.211 fatcat:jiguv4kmpfagbkmukobfbe4vca