The Left Regular Representation of a Semigroup

• Main Author: Rowe, Barry James
• Other Authors: Rosenthal, Peter
• Language: en_ca
• Published: 2011
• Subjects: Operator Theory; Semigroups; 0405
• Online Access: http://hdl.handle.net/1807/31922

As with groups, one can study the left regular representation of a semigroup. If one considers such representations, then it is natural to ask similar questions to the group case. We start by formulating several questions in the semigroup case and then work towards understanding the structure of the representations given. We present results describing what the elements of the image under the representation map can look like (the semigroup problem), whether or not two semigroups will give isomorphic representations (the isomorphism problem), and whether or not the representation of a semigroup is reflexive (the reflexivity problem). This research has been funded in part by a scholarship from the Natural Sciences and Engineering Research Council of Canada.