Center of the semigroup algebra of a finite inverse semigroup over the field of complex numbers

Abstract

In the semigroup algebra A of a finite inverse semigroup S over the field of complex numbers to an indempotent e there is assigned the sum σ(e)=e+∑(−1)^Ke_L1⋯e_iK, where e_i,...,e_m are maximal preidempotents of the idempotent e, and the summation goes over all nonempty subsets {i₁,...,i_k} of the set {1,...m} Then for any class K of conjugate group elements of the semigroup S the element K=∑a·(a⁻¹a) (the summation goes over all a∈g) is a central element of the algebra A, and the set {K} of all possible such elements is a basis for the center of the algebra A.