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