Results 141 to 150 of about 285 (163)

On spherical ideals of Borel subalgebras

Archiv der Mathematik, 2005
Let \(G\) be a connected reductive complex algebraic group, and \(B\) be a Borel subgroup of \(G\) with unipotent radical \(B_u\). Let \({\mathfrak g}\), \({\mathfrak b}\), and \({\mathfrak b}_u\) denote the Lie algebras of \(G\), \(B\), and \(B_u\) respectively.
Panyushev, Dmitri, Roehrle, Gerhard
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Cartan subalgebras, Borel subalgebras and parabolic subalgebras

Springer Monographs in Mathematics, 2005
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Borel subalgebras of the Witt algebra

Acta Mathematica Sinica, English Series, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hao Chang
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On Borel subalgebras of quantum groups

, 2016
Diese Arbeit beschäftigt sich mit der Klassifikation aller Rechtscoidealunteralgebren C der Quantengruppen bei generischem q, mit der folgenden Eigenschaft: Alle endlichdimensionalen irreduziblen Darstellungen von C sind eindimensional und C ist maximal mit dieser Eigenschaft. Solche Rechtscoidealunteralgebren nennen
Vocke, Karolina
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Borel Subalgebras of Schur Superalgebras

Algebra and Logic, 2005
Summary: It is proved that any Schur superalgebra is representable as a product of two Borel subalgebras of that superalgebra, which are symmetric w.r.t. its natural anti-isomorphism (Bruhat-Tits decomposition). This readily implies that any simple module is uniquely defined by its highest weight, and all other weights are strictly less than the ...
A N Zubkov
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Varieties of Borel subalgebras for the Jacobson–Witt Lie algebras

Forum Mathematicum, 2023
AbstractLetW⁢(n){W(n)}be the Jacobson–Witt algebra over algebraic closed field𝕂{\mathbb{K}}with characteristicp>2{p>2}. In [K. Ou and B. Shu, Borel subalgebras of restricted Cartan-type Lie algebras, J. Algebra Appl. 21 2022, 11, Paper No. 2250210], we introduced the so-called B-subalgebra ofW⁢(n){W(n)}, which serves as an analog of the Borel ...
Ke Ou, Bin Shu
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Exact borel subalgebras of quasi-hereditary algebras. II

Communications in Algebra, 1995
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Steffen KÖNIG
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Algebraic Lie algebras with complete Borel subalgebras

Linear and Multilinear Algebra, 2009
In this article we prove that an algebraic Lie algebra over an algebraically closed field of characteristic 0 is complete if its Borel subalgebras are complete. Thus the study on complete Lie algebras may somewhat be reduced to that on solvable complete ones.
Dengyin Wang, Shikun Ou
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Conjugation-uniqueness of exact Borel subalgebras

Science in China Series A: Mathematics, 1999
Exact 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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Strong Exact Borel Subalgebras of Quasi-hereditary Algebras and Abstract Kazhdan–Lusztig Theory

Advances in Mathematics, 1999
Strong exact Borel subalgebras and strong Δ-subalgebras are shown to exist for quasi-hereditary algebras which possess exact Borel subalgebras and Δ-subalgebras.
Steffen KÖNIG
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