On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces
, 2013 Let g=g0⊕g1 be a Z2-graded Lie algebra. We study the posets of abelian subalgebras of g1 which are stable w. r. t. a Borel subalgebra of g0. In particular, we find a natural parametrization of maximal elements and dimension formulas for them.
P. Cellini +7 more
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Borel subalgebras of alternative and Jordan algebras
Journal of Algebra, 1970 In the above paper the Borel-Morozov theorem, which states that in a semisimple complex Lie algebra the group of inner automorphism acts transitively on the Borel (= maximal solvable) subalgebras, is extended to alternative and Jordan algebras. As it turns out, these extensions are valid over any base field \(k\) of characteristic not 2 or 3.
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Abelian ideals of a Borel subalgebra and root systems [PDF]
Journal of the European Mathematical Society, 2014 Let \mathfrak g be a simple Lie algebra and \mathfrak {Ab}^o the poset of non-trivial abelian ideals of a fixed Borel subalgebra of
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An Algorithm for Computing Ideals and Conjugacy Classes of Subalgebras of Borel Subalgebras
In this article, we present a constructive procedure for determining all ideals of the Borel subalgebra of a complex semisimple Lie algebra from its root system or, equivalently, its Dynkin diagram. The proposed algorithmic approach has been implemented in Maple.
Asghar, Nimra Sher, Azad, Hassan
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The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities. [PDF]
Calc Var Partial Differ Equ, 2023 Sodini GE.
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Remarks on the abelian ideals of a Borel subalgebra
, 2013 Let $\frb$ be a fixed Borel subalgebra of a finite-dimensional complex simple Lie algebra $\frg$. The Shi bijection associates to every ad-nilpotent ideal $\fri$ of $\frb$ a region $V_{\fri}$. In this paper, we show that $\fri$ is abelian if and only if $V_{\fri}\cap 2A$ is empty, if and only if the volume of $V_{\fri}\cap 2A$ equals to that of $A ...
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Bott-Borel-Weil theory and Bernstein-Gel'Fand-Gel'Fand reciprocity for the Lie superalgebras
, 2016 The main focus of this paper is Bott-Borel-Weil (BBW) theory for basic classical Lie superalgebras. We take a purely algebraic self-contained approach to the problem.
Coulembier, Kevin
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Strong Exact Borel Subalgebras of Quasi-Hereditary Algebras
Journal of Algebra, 2000 Exact and strong Borel subalgebras of quasi-hereditary algebras were introduced by the reviewer [see Math. Z. 220, No. 3, 399-426 (1995; Zbl 0841.16013)] to mimick the situation for Lie algebras. Existence is granted for blocks of category \(\mathcal O\) and in a few other situations, but not in general. A natural problem is uniqueness.
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Exact Borel subalgebras of path algebras of quivers of Dynkin type A
Hereditary algebras are quasi-hereditary with respect to any adapted partial order on the indexing set of the isomorphism classes of their simple modules. For any adapted partial order on {1, ...
Thuresson, Markus
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Unipotent Radicals of the Standard Borel and Parabolic Subgroups in Quantum Special Linear Groups [PDF]
, 2014 In this dissertation we find noncommutative analogues of the coordinate rings of the unipotent radicals of the standard Borel and standard parabolic subgroups in quantum special linear groups.
Jaramillo, Andrew Cecil
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