Semisymmetric Graphs Defined by Finite-Dimensional Generalized Kac–Moody Algebras

Yang, Fuyuan; Sun, Qiang; Zhang, Chao

doi:10.1007/s40840-022-01380-3

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2023

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“…Concretely, the applications of the graphs for the study of linear operators and algebras [6][7][8][9][10][11][12]. We highlight that this topic is currently very active as some recently published articles show [13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs

et al. 2023

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In this work, we study a linear operator f on a pre-Euclidean space V by using properties of a corresponding graph. Given a basis B of V, we present a decomposition of V as an orthogonal direct sum of certain linear subspaces {Ui}i∈I, each one admitting a basis inherited from B, in such way that f=∑i∈Ifi. Each fi is a linear operator satisfying certain conditions with respect to Ui. Considering this new hypothesis, we assure the existence of an isomorphism between the graphs of f relative to two different bases. We also study the minimality of V by using the graph of f relative to B.

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