caa a22 4500 60616121X CHVBK 20210128100633.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9499-2 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9499-2 Classification of Simple Weight Modules Over the 1-Spatial Ageing Algebra [Elektronische Daten] [Rencai Lü, Volodymyr Mazorchuk, Kaiming Zhao] In this paper we use Block's classification of simple modules over the first Weyl algebra to obtain a complete classification of simple weight modules, in particular, of Harish-Chandra modules, over the 1-spatial ageing algebra 𝔞 𝔤 𝔢 ( 1 ) $\mathfrak {age(1)}$ . Most of these modules have infinite dimensional weight spaces and so far the algebra 𝔞 𝔤 𝔢 ( 1 ) $\mathfrak {age(1)}$ is the only Lie algebra having simple weight modules with infinite dimensional weight spaces for which such a classification exists. As an application we classify all simple weight modules over the (1+1)-dimensional space-time Schrödinger algebra S $\mathcal {S}$ that have a simple 𝔞 𝔤 𝔢 ( 1 ) $\mathfrak {age(1)}$ -submodule thus constructing many new simple weight S $\mathcal {S}$ -modules. Springer Science+Business Media Dordrecht, 2014 Weight module nationallicence Schrödinger algebra nationallicence Ageing algebra nationallicence Highest weight module nationallicence Lü Rencai Department of Mathematics, Soochow University, Suzhou, P. R. China aut Mazorchuk Volodymyr Department of Mathematics, Uppsala University, SE-751 06, Box 480, Uppsala, Sweden aut Zhao Kaiming Department of Mathematics, Wilfrid Laurier University, N2L 3C5, Waterloo, Ontario, Canada aut Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 381-395 1386-923X 18:2<381 2015 18 10468 https://doi.org/10.1007/s10468-014-9499-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9499-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lü Rencai Department of Mathematics, Soochow University, Suzhou, P. R. China aut NATIONALLICENCE 700 1- Mazorchuk Volodymyr Department of Mathematics, Uppsala University, SE-751 06, Box 480, Uppsala, Sweden aut NATIONALLICENCE 700 1- Zhao Kaiming Department of Mathematics, Wilfrid Laurier University, N2L 3C5, Waterloo, Ontario, Canada aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 381-395 1386-923X 18:2<381 2015 18 10468