Abelian ideals and amazing roots
نویسندگان
چکیده
منابع مشابه
Abelian Ideals of a Borel Subalgebra and Long Positive Roots
Let b be a Borel subalgebra of a simple Lie algebra g. Let Ab denote the set of all Abelian ideals of b. It is easily seen that any a ∈ Ab is actually contained in the nilpotent radical of b. Therefore a is determined by the the corresponding set of roots. More precisely, let t be a Cartan subalgebra of g lying in b and let ∆ be the root system of the pair (g, t). Choose ∆, the system of positi...
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Let b be a Borel subalgebra of a simple Lie algebra g. LetAb denote the set of all Abelian ideals of b. It is easily seen that any a ∈Ab is actually contained in the nilpotent radical of b. Therefore a is determined by the the corresponding set of roots. More precisely, let t be a Cartan subalgebra of g lying in b and let ∆ be the root system of the pair (g, t). Choose the system of positive ro...
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For symplectic Lie algebras sp(2n,C), denote by b and n its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of b and the cohomology of n with trivial coefficients. By this relationship, we can enumerate the number of abelian ideals of b with certain dimension via the Poincaré polynomials of Weyl groups of type An−1 and Cn.
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15 صفحه اولStickelberger ideals and Fitting ideals of class groups for abelian number fields
In this paper, we determine completely the initial Fitting ideal of the minus part of the ideal class group of an abelian number field over Q up to the 2-component. This answers an open question of Mazur and Wiles [11] up to the 2-component, and proves Conjecture 0.1 in [8]. We also study Brumer’s conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular...
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2017
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x17501051