Results 131 to 140 of about 381 (158)

The Cartan matrix of the Schur algebra S(2, r)

Archiv Der Mathematik, 2001
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On Toda system with Cartan matrix $G_2$

Proceedings of the American Mathematical Society, 2015
Summary: We consider the Toda system \[ \Delta u_i + \sum _{j = 1}^2 a_{ij}e^{u_j} = 4\pi \gamma _{i}\delta _{0}\text{ in }\mathbb{R}^2, \quad \int _{\mathbb{R}^2}e^{u_i} dx < \infty ,\text{ for } i=1,2, \] where \( \gamma _{i} > -1\), \( \delta _0\) is the Dirac measure at 0, and the coefficients \( a_{ij}\) are of the Cartan matrix of rank 2: \( A_2,
Ao, Weiwei, Lin, Chang-Shou, Wei, Juncheng   +2 more
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The spectral radius of the Coxeter transformations for a generalized Cartan matrix [PDF]

Mathematische Annalen, 1994
This work concerns the eigenvalues (more precisely, the spectral radius) of the Coxeter transformations \(C = C(A, \pi)\) for a generalized Cartan matrix \(A\) [for such matrices see \textit{V. Kac} ``Infinite dimensional Lie algebras'', 2nd ed. Cambridge Univ. Press (1985; Zbl 0574.17010); 3rd ed. (1990; Zbl 0716.17022)].
Claus Michael Ringel, Ringel Claus Michael   +1 more
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Cartan Matrix for the Finite Symplectic Group Sp(6, 3)

Algebra Colloquium, 2003
The Cartan matrix for \(\text{Sp}(6,3)\) in characteristic 3 is computed from the Brauer character table.
Jiachen Ye
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Lie algebras of an affinization of a generalized Cartan matrix

Archiv Der Mathematik, 1998
The author defines the affinized Lie algebra \(g_a(A^{[1]})\) of \(A^{[1]}\), a 1-fold affinization of a generalized Cartan matrix \(A\) of finite or affine type and proves that the affinized Lie algebra \(g_a (A^{[1]})\) and the radical free contragredient Lie algebra \(g_c (A^{[1]})\) are homomorphic images of a Lie algebra with finitely generated ...
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Encoding the Cartan Matrix

1995
Unless otherwise indicated it is assumed in the remainder of this text that char k = 0 and that q is an indeterminate.
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The inverse of a Cartan matrix

1992
The Cartan matrix is treated as a matrix modelled on the incidence matrix of a tree. Moreover, an explicit formula for the entries of the inverse of a Cartan matrix is given.
Lusztig, George, Tits, Jacques
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Some results on the cartan matrix of a frobenius algebra

Communications in Algebra, 1996
Let F be a field and A a Frobenius algebra over F. The Jacobson radical of A is denoted by J = J(A) and the kth socle of A by S k (A). Let [Abar]=A/J k or A/S k (A). This article gives new interesting relations between the Cartan matrix of A and that of [Abar].
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On the Cartan matrix of a left Artinian ring

1992
The Cartan matrix \(C\) of a left Artinian ring \(R\) does not contain a sufficient amount of information for deciding whether \(R\) has finite or infinite left global dimension. Nevertheless the matrix \(C\) can give some important information about the global dimension.
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The (q, t)-Cartan matrix specialized at $$q=1$$ and its applications

Mathematische Zeitschrift, 2023
Se-Jin Oh, Kashiwara Masaki, Oh Se-Jin   +2 more
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