5 papers
Irreducible tensor product modules over the Takiff Lie algebra for
Yu Qiao, Xiaoyu Zhu
In this paper, we construct a class of non-weight modules over the Takiff by taking the tensor products of the irreducible free -mod…
Combinatorics of monoidal actions in Lie-algebraic context
Volodymyr Mazorchuk, Xiaoyu Zhu
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple fi…
Combinatorics of infinite rank module categories over finite dimensional -modules in Lie-algebraic context
Volodymyr Mazorchuk, Xiaoyu Zhu
We determine the combinatorics of transitive module categories over the monoidal category of finite dimensional -modules which arise when acting by the latter mono…
Infinite rank module categories over finite dimensional -modules in Lie-algebraic context
Volodymyr Mazorchuk, Xiaoyu Zhu
We study locally finitary realizations of simple transitive module categories of infinite rank over the monoidal category of finite dimensional modules for the comple…
Induced modules and central character quotients for Takiff
Xiaoyu Zhu
We construct a large new family of simple modules over Takiff . We prove that the quotient of the universal enveloping algebra of the Takiff Lie algebra for $\ma…