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• W3035595596 abstract "Abstract Cartan matrices, quasi-Cartan matrices and associated upper triangular Gram matrices control important combinatorial aspects of Lie theory and representation theory of associative algebras. We provide a graph theoretic proof of the fact that the absolute values of the coefficients of a non-negative quasi-Cartan matrix A as well as of its (minimal) symmetrizer D are bounded by 4, and that the analogous bound in case of the associated Gram matrix G ˇ A is 8. Moreover, we show that D (and G ˇ A ) has at least one diagonal coefficient equal to 1. We describe some other restrictions and interrelations between the coefficients of A , D and G ˇ A , and the corank and other properties of A relevant in Lie theory. We apply our results to construct an algorithm by which we classify all non-negative quasi-Cartan matrices of small sizes." @default.
• W3035595596 created "2020-06-19" @default.
• W3035595596 creator A5011873433 @default.
• W3035595596 creator A5035248678 @default.
• W3035595596 date "2020-06-01" @default.
• W3035595596 modified "2023-09-30" @default.
• W3035595596 title "Coefficients of non-negative quasi-Cartan matrices, their symmetrizers and Gram matrices" @default.
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• W3035595596 doi "https://doi.org/10.1016/j.dam.2020.05.022" @default.
• W3035595596 hasPublicationYear "2020" @default.
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