Induced modules and central character quotients for Takiff \mathfraksl₂

2024/01/31 by Zhu, Xiaoyu · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2401.17627

Abstract

We construct a large new family of simple modules over Takiff \mathfraksl₂. We prove that the quotient of the universal enveloping algebra of the Takiff Lie algebra for \mathfraksl₂ by the ideal generated by a non-trivial central character is a simple algebra. In the case of the trivial central character, we show that the corresponding ideal is primitive by explicitly constructing a simple module whose annihilator coincides with that ideal. Together with the annihilators of simple \mathfraksl₂-modules, we expect that the above ideals exhaust all primitive ideal.

Cited by

• Infinite rank module categories over finite dimensional sl 2 \mathfrak sl₂ German sl 2-modules in Lie algebraic-context

Related

• Simple modules over the Takiff Lie algebra for \mathfraksl₂
• Annihilators of simple tensor modules
• Typical representations of Takiff superalgebras
• Category O for Takiff Lie algebras
• Primitive ideals in the affinoid enveloping algebras of semisimple Lie algebras