Results 1 to 10 of about 297 (147)
Cartan invariant matrices for finite monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $M$ be a finite monoid. In this paper we describe how the Cartan invariant matrix of the monoid algebra of $M$ over a field $\mathbb{K}$ of characteristic zero can be expressed using characters and some simple combinatorial statistic.
Nicolas M. Thiéry
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Coefficients of non-negative quasi-Cartan matrices, their symmetrizers and Gram matrices
Discrete Applied Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrzej Mroz
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Eigenvector matrices of Cartan matrices for finite groups
Journal of Algebra, 2007 Let \(p\) be a prime, let \(G\) be a finite group, and let \((K,R,F)\) be a \(p\)-modular system which is sufficiently large for \(G\). Moreover, let \(B\) be a block of the group algebra \(FG\) with defect group \(D\) and Cartan matrix \(C_B\). The author is interested in relations between \(R_B\), the set of eigenvalues of \(C_B\), and \(E_B\), the ...
Tomoyuki Wada
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Cellular algebras and Cartan matrices
Linear Algebra and Its Applications, 2003 This paper studies the cellular algebras with respect to some restriction on their Cartan matrices. The most strong restriction happens when the Cartan matrix has determinant one and all of its eigenvalues are integers. The authors prove that in this case the algebra is semisimple.
Changchang Xi
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Rationality of Eigenvalues of Cartan Matrices in Finite Groups
Journal of Algebra, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Masafumi Murai, Tomoyuki Wada
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Finite Quantum Groups and Cartan Matrices
Advances in Mathematics, 2000 This paper considers a class of Hopf algebras over an algebraically closed field \(k\) having as an invariant a generalized Cartan matrix. Let \(\Gamma\) be a fixed finite Abelian group, \(V\) a finite-dimensional Yetter-Drinfeld module over \(k\Gamma\) with a \(k\)-basis \(\{x_1,\dots,x_\theta\}\).
Nicolas Andruskiewitsch +1 more
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Cartan matrices of selfinjective algebras of tubular type
Open Mathematics, 2004 The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. One of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras. Recently, the class
Białkowski Jerzy
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Combinatorics for Graded Cartan Matrices of the Iwahori-Hecke Algebra of Type A [PDF]
Annals of Combinatorics, 2013 A $q$-analogue of combinatorics concerning the Cartan matrix for the Iwahori-Hecke algebra of type $A$ is investigated. We give several descriptions for the determinant of the graded Cartan matrix, which imply some combinatorial identities. A conjectural expression for the elementary divisors is also presented.
Takeshi Suzuki, Hiro-Fumi Yamada
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Elementary divisors of Cartan matrices for symmetric groups
Journal of the Mathematical Society of Japan, 2006 The purpose of this paper is to give a simple expression of the elementary divisors of the cartan matrices for the symmetric groups.
Hiro-Fumi Yamada
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Inverses of Cartan matrices of Lie algebras and Lie superalgebras
Linear Algebra and Its Applications, 2017 We derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations.
Yi Ming Zou
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