Results 161 to 170 of about 1,593,546 (194)

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)].
Ringel, Claus Michael
exaly   +6 more sources

Cokernels of the Cartan matrix and stratifying systems [PDF]

Communications in Algebra, 2019
We study the cokernel of the application given by the Cartan Matrix $C_Λ$ of a finite dimensional $k$-algebra $Λ.$ This produces a finitely generated abelian group, the Cartan group $G_Λ,$ which is invariant under derived equivalences. We are interested in the case when $G_Λ$ is finite.
Octavio Mendoza
exaly   +3 more sources

The Roots of Exceptional Modular Lie Superalgebras with Cartan Matrix [PDF]

Arnold Mathematical Journal, 2020
For each of the exceptional Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots of and the corresponding Chevalley basis for one of the inequivalent Cartan matrices, the one corresponding to the greatest number of mutually orthogonal isotropic odd simple roots.
Jin Shang, Sofiane Bouarroudj, Dimitry Alexander Leites   +2 more
exaly   +3 more sources

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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.
Lenzing, Helmut, Meltzer, Hagen
openaire   +1 more source

Rationality of Eigenvalues of Cartan Matrices in Finite Groups [PDF]

Journal of Algebra, 2002
We study the case in which eigenvalues and elementary divisors of a Cartan matrix of a p-block B of a finite group coincide. In several cases we prove the coincidence occurs if and only if the Perron–Frobenius eigenvalue of the Cartan matrix is equal to ...
Masafumi Murai, Tomoyuki Wada
exaly   +2 more sources

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
openaire   +2 more sources

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.
openaire   +1 more source

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.
Liu, Ailan, Ye, Jiachen
exaly   +3 more sources

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
openaire   +2 more sources

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].
openaire   +1 more source