Results 1 to 10 of about 158 (119)

Ad-nilpotent ideals of a Borel subalgebra II

Journal of Algebra, 2002
AmsTex file, 38 pages; revised version. To appear in Advances in Mathematics under the title "Abelian ideals of Borel subalgebras and affine Weyl groups"
Paola Cellini, Paolo Papi
exaly   +6 more sources

ad-Nilpotent ideals of a Borel subalgebra

Journal of Algebra, 2000
Let \({\mathfrak g}\) be a finite dimensional complex simple Lie algebra, \({\mathfrak h}\) a Cartan subalgebra of \({\mathfrak g}\), and \(\Delta^+\) a positive root system. Also let \(\widehat{\Delta}^+\) and \(\widehat{W}\) be the affine positive real root system and affine Weyl group, respectively.
Paola Cellini, Paolo Papi
exaly   +3 more sources

Abelian Ideals of a Borel Subalgebra and Root Systems, II [PDF]

Algebras and Representation Theory, 2019
12 ...
exaly   +4 more sources

Glorious pairs of roots and Abelian ideals of a Borel subalgebra [PDF]

Journal of Algebraic Combinatorics, 2019
20 ...
exaly   +3 more sources

ad-nilpotent ideals of a Borel subalgebra: generators and duality

Journal of Algebra, 2004
It was shown by Cellini and Papi that an ad-nilpotent ideal determines certain element of the affine Weyl group, and that there is a bijection between the ad-nilpotent ideals and the integral points of a simplex with rational vertices. We give a description of the generators of ad-nilpotent ideals in terms of these elements, and show that an ideal has $
exaly   +4 more sources

On the automorphisms of the Drinfel'd double of a Borel Lie subalgebra

Journal of Algebra
Let ${\mathfrak g}$ be a complex simple Lie algebra with Borel subalgebra ${\mathfrak b}$. Consider the semidirect product $I{\mathfrak b}={\mathfrak b}\ltimes{\mathfrak b}^*$, where the dual ${\mathfrak b}^*$ of ${\mathfrak b}$, is equipped with the coadjoint action of ${\mathfrak b}$ and is considered as an abelian ideal of $I{\mathfrak b}$.
Nicolas Ressayre
exaly   +5 more sources

The Existence of Affine Structures on the Borel Subalgebra of Dimension 6

ComTech, 2021
The notion of affine structures arises in many fields of mathematics, including convex homogeneous cones, vertex algebras, and affine manifolds. On the other hand, it is well known that Frobenius Lie algebras correspond to the research of homogeneous ...
Edi Kurniadi, Ema Carnia, Herlina Napitupulu   +2 more
doaj   +1 more source

On locally analytic vectors of the completed cohomology of modular curves

Forum of Mathematics, Pi, 2022
We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of $\mathfrak {gl}_2(\mathbb {Q}_p)$ .
Lue Pan
doaj   +1 more source

Root Polytopes and Borel Subalgebras [PDF]

International Mathematics Research Notices, 2014
revised version, accepted for publication in ...
CELLINI, PAOLA, Marietti, Mario
openaire   +3 more sources

A Family of New Borel Subalgebras of Quantum Groups [PDF]

Algebras and Representation Theory, 2020
AbstractWe construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the standard Borel subalgebras expected from Lie theory, but in a quantum group there are many more.
Lentner, Simon, Vocke, Karolina
openaire   +2 more sources