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Integral Pairings and Dynkin Indices
Author(s) -
Braden H. W.
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-43.2.313
Subject(s) - mathematics , dynkin diagram , simple (philosophy) , integer (computer science) , subalgebra , index (typography) , pure mathematics , algebra over a field , algebraic number , lie algebra , mathematical analysis , computer science , philosophy , epistemology , world wide web , programming language
We review two related notions of index introduced by Dynkin, one the index of a subgroup or subalgebra in a semi‐simple group or algebra and the other being the index of a linear representation of a semi‐simple Lie algebra. Amongst other results we give a simple algebraic proof of Dynkin's theorem that this first index is an integer.