2022-12-08T00:29:17Zhttps://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, AkihideAssociation 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)journal articleSPRINGER2016-11application/pdfJOURNAL OF ALGEBRAIC COMBINATORICS3445876020925-9899AA10868319https://soar-ir.repo.nii.ac.jp/record/19865/files/Modular_adjacency_algebras_standard_representations.pdfeng10.1007/s10801-016-0681-yhttps://doi.org/10.1007/s10801-016-0681-yThe final publication is available at link.springer.com