A Class of Nonunitary, Finite Dimensional Representations of the Euclidean Algebra 𝔢(2)

Abstract

Abstract In this article, we examine the finite dimensional representations of the Euclidean algebra 𝔢(2) that are obtained by embedding 𝔢(2) into 𝔰𝔩3, the Lie algebra of traceless 3 × 3 matrices. We show that the finite dimensional, irreducible representations of 𝔰𝔩3 restricted to 𝔢(2) are indecomposable and, when possible, we give graphical descriptions of these 𝔢(2) representations. Key Words: Euclidean algebraIndecomposable representationsTensor product decompositionMathematics Subject Classification: Primary 17B10Secondary 17B30 Notes Communicated by D. K. Nakano.