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Lie algebras

George Seligman (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Malcev-Moduln.

Renate Carlsson (1976)

Journal für die reine und angewandte Mathematik

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma (2024)

Czechoslovak Mathematical Journal

We construct a family of non-weight modules which are free U ( 𝔥 ) -modules of rank 2 over the N = 1 super Schrödinger algebra in ( 1 + 1 ) -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free U ( 𝔥 ) -modules of rank 2 over 𝔬𝔰𝔭 ( 1 | 2 ) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

On bounded generalized Harish-Chandra modules

Ivan Penkov, Vera Serganova (2012)

Annales de l’institut Fourier

Let 𝔤 be a complex reductive Lie algebra and 𝔨 𝔤 be any reductive in 𝔤 subalgebra. We call a ( 𝔤 , 𝔨 ) -module M bounded if the 𝔨 -multiplicities of M are uniformly bounded. In this paper we initiate a general study of simple bounded ( 𝔤 , 𝔨 ) -modules. We prove a strong necessary condition for a subalgebra 𝔨 to be bounded (Corollary 4.6), i.e. to admit an infinite-dimensional simple bounded ( 𝔤 , 𝔨 ) -module, and then establish a sufficient condition for a subalgebra 𝔨 to be bounded (Theorem 5.1). As a result we are able to...

On category 𝒪 for cyclotomic rational Cherednik algebras

Iain G. Gordon, Ivan Losev (2014)

Journal of the European Mathematical Society

We study equivalences for category 𝒪 p of the rational Cherednik algebras 𝐇 p of type G ( n ) = ( μ ) n 𝔖 n : a highest weight equivalence between 𝒪 p and 𝒪 σ ( p ) for σ 𝔖 and an action of 𝔖 on an explicit non-empty Zariski open set of parameters p ; a derived equivalence between 𝒪 p and 𝒪 p ' whenever p and p ' have integral difference; a highest weight equivalence between 𝒪 p and a parabolic category 𝒪 for the general linear group, under a non-rationality assumption on the parameter p . As a consequence, we confirm special cases of conjectures...

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