Category O for Takiff sl_2

Abstract

We investigate various ways to define an analogue of BGG category $\mathcal{O}$ for the non-semi-simple Takiff extension of the Lie algebra ${\mathfrak{sl}}_2$. We describe Gabriel quivers for blocks of these analogues of category $\mathcal{O}$ and prove extension fullness of one of them in the category of all modules.

Fixed typos in Corollary 28

References in corpus (1)

• Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules

Cited by in corpus (2)

• Lie algebra modules which are locally finite over the semi-simple part
• ${\mathfrak{sl}}_2$-Harish-Chandra modules for ${\mathfrak{sl}}_2⋉L(4)$