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Defining Relations for Lie Superalgebras with Cartan Matrix [PDF]

Czechoslovak Journal of Physics, 1997
We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple ℤ-graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered.
Pavel Grozmann, D. Leites
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The Cartan matrix of a centralizer algebra

Proceedings - Mathematical Sciences, 2012
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective indecomposable modules, simple modules and Cartan matrices.
U. Dubey, A. Prasad, P. Singla
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Rational cohomology and Cartan matrix

Topology and its Applications
Nan Gao, Chi-Heng Zhang, Zi-Cheng Cheng
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On Toda system with Cartan matrix

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,
Weiwei Ao, Changshou Lin, Juncheng Wei
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The Cartan matrix of the Schur algebra S(2, r)

Archiv der Mathematik, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Henke
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Space-curve Cartan matrix and exact differentiability of the curvature and torsion

Mechanics based design of structures and machines, 2022
In formulation of beam-vibration equations, curvature of space curves is used to define the strain energy and elastic forces. Only in special cases, the curvature and torsion can be associated with derivatives of angles.
A. Shabana
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Exceptional Sequences Determined by their Cartan Matrix

Algebras and Representation Theory, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Lenzing, H. Meltzer
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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.
Ailan Liu, Jiachen Ye
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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].
Zeng Jiwen
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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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