Simple Schrödinger modules which are locally finite over the positive part

Zhang, Xiufu; Cheng, Yongsheng

doi:10.1016/j.jpaa.2014.09.029

Cited by 30 publications

(15 citation statements)

References 28 publications

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“…They also characterize simple Virasoro modules that are locally finite over a positive part. Motivated by [30], new simple modules for the Virasoro algebra and its extensions have been studied [8,9,26,28,37]. Superconformal algebras have a long history in mathematical physics.…”

Section: Introductionmentioning

confidence: 99%

Simple restricted modules for Neveu-Schwarz algebra

2020

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In this paper, we give a construction of simple modules generalizing both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We establish a 1-1 correspondence between simple restricted Neveu-Schwarz modules and simple modules of a family of finite dimensional solvable Lie superalgebras associated to the Neveu-Schwarz algebra. Moreover, for two of these superalgebras all simple modules are classified.

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Section: Introductionmentioning

confidence: 99%

Simple restricted modules for Neveu-Schwarz algebra

2020

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“…In [17], the author studied the finite dimensional indecomposable modules of the Schrödinger algebra. The BGG category O of the Schrödinger algebra was considered in [12], the simple non-singular Whittaker modules and quasi-Whittaker modules were classified in [18,9]. In [7], a classification of simple weight U (s)-modules is given.…”

Section: Introductionmentioning

confidence: 99%

“…Existence of simple singular Whittaker A-modules. It is conjectured that there is no simple singular Whittaker module for the algebra A [18,Conjecture 4.2]. We construct a family of such A-modules (Proposition 4.6).…”

Section: Introductionmentioning

confidence: 99%

The Universal Enveloping Algebra of the Schrödinger Algebra and its Prime Spectrum

Bavula¹,

Lü²

2018

Can. math. bull.

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The prime, completely prime, maximal, and primitive spectra are classified for the universal enveloping algebra of the Schrödinger algebra. The explicit generators are given for all of these ideals. A counterexample is constructed to the conjecture of Cheng and Zhang about nonexistence of simple singular Whittaker modules for the Schrödinger algebra (and all such modules are classified). It is proved that the conjecture holds ‘generically’.

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“…They defined a class of modules called quasi-Whittaker modules. Different from [16], quasi-Whittaker modules are not induced by the Borel subalgebra of the Schrödinger algebra, but its Heisenberg subalgebra. Similar work for the Euclidean Lie algebra was done later in [17].…”

Section: Introductionmentioning

confidence: 99%