{"title":"${K}_{4}^{\\素数}$有限Verma模复合体的同调计算","authors":"Lucia Bagnoli","doi":"10.1007/s10468-022-10176-9","DOIUrl":null,"url":null,"abstract":"<div><p>We compute the homology of the complexes of finite Verma modules over the annihilation superalgebra <span>\\(\\mathcal {A}({K}_{4}^{\\prime })\\)</span>, associated with the conformal superalgebra <span>\\({K}_{4}^{\\prime }\\)</span>, obtained in Bagnoli and Caselli (J. Math. Phys. <b>63</b>, 091701, 2022). We use the computation of the homology in order to provide an explicit realization of all the irreducible quotients of finite Verma modules over <span>\\(\\mathcal {A}({K}_{4}^{\\prime })\\)</span>.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-022-10176-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Computation of the Homology of the Complexes of Finite Verma Modules for \\\\({K}_{4}^{\\\\prime }\\\\)\",\"authors\":\"Lucia Bagnoli\",\"doi\":\"10.1007/s10468-022-10176-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We compute the homology of the complexes of finite Verma modules over the annihilation superalgebra <span>\\\\(\\\\mathcal {A}({K}_{4}^{\\\\prime })\\\\)</span>, associated with the conformal superalgebra <span>\\\\({K}_{4}^{\\\\prime }\\\\)</span>, obtained in Bagnoli and Caselli (J. Math. Phys. <b>63</b>, 091701, 2022). We use the computation of the homology in order to provide an explicit realization of all the irreducible quotients of finite Verma modules over <span>\\\\(\\\\mathcal {A}({K}_{4}^{\\\\prime })\\\\)</span>.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-12-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10468-022-10176-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10468-022-10176-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-022-10176-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computation of the Homology of the Complexes of Finite Verma Modules for \({K}_{4}^{\prime }\)
We compute the homology of the complexes of finite Verma modules over the annihilation superalgebra \(\mathcal {A}({K}_{4}^{\prime })\), associated with the conformal superalgebra \({K}_{4}^{\prime }\), obtained in Bagnoli and Caselli (J. Math. Phys. 63, 091701, 2022). We use the computation of the homology in order to provide an explicit realization of all the irreducible quotients of finite Verma modules over \(\mathcal {A}({K}_{4}^{\prime })\).
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