2022-12-03T05:39:28Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000198652021-09-02T06:24:49Z1169:1170Modular adjacency algebras, standard representations, and p-ranks of cyclotomic association schemesHanaki, AkihideThe final publication is available at link.springer.comAssociation schemeCyclotomic schemeRepresentationp-RankFirst Online: 31 March 2016In this paper, we consider cyclotomic association schemes S = Cyc(p(a), d). We focus on the adjacency algebra of S over algebraically closed fields K of characteristic p. If p equivalent to 1 (mod d), p equivalent to -1 (mod d), or d is an element of {2, 3, 4, 5, 6}, we identify the adjacency algebra of S over K as a quotient of a polynomial ring over an admissible ideal. In several cases, we determine the indecomposable direct sum decomposition of the standard module of S. As a consequence, we are able to compute the p-rank of several specific elements of the adjacency algebra of S over K.ArticleJOURNAL OF ALGEBRAIC COMBINATORICS. 44(3):587-602 (2016)SPRINGER2016-11engjournal articleAMhttp://hdl.handle.net/10091/00020626https://soar-ir.repo.nii.ac.jp/records/19865https://doi.org/10.1007/s10801-016-0681-y10.1007/s10801-016-0681-y0925-9899AA10868319JOURNAL OF ALGEBRAIC COMBINATORICS443587602https://soar-ir.repo.nii.ac.jp/record/19865/files/Modular_adjacency_algebras_standard_representations.pdfapplication/pdf292.7 kB2017-03-31