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A classification of the simple weight modules is given for the (6-dimensional) Euclidean Lie algebra ????(3) = ????????2⋉V3. As an intermediate step, a classification of all simple modules is given… Click to show full abstract
A classification of the simple weight modules is given for the (6-dimensional) Euclidean Lie algebra ????(3) = ????????2⋉V3. As an intermediate step, a classification of all simple modules is given for the centralizer C of the Cartan element H (in the universal enveloping algebra ???? = U(????(3))). Generators and defining relations for the algebra C are found (there are three quadratic relations and one cubic relation). The algebra C is a Noetherian domain of Gelfand-Kirillov dimension 5. Classifications of prime, primitive, completely prime, and maximal ideals are given for the algebra U .
Journal Title: Journal of Mathematical Physics
Year Published: 2017
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