Results 151 to 160 of about 405 (171)
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Borel subalgebras of the Witt algebra
Acta Mathematica Sinica, English Series, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yao, Yu Feng, Chang, Hao
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Borel subalgebras of restricted Cartan -Type Lie algebras
Journal of Algebra and Its Applications, 2021It is still an open problem to determine the conjugacy classes of Borel subalgebras of non-classical type Lie algebras. In this paper, we prove that there are at least 2 conjugacy classes of Borel subalgebras as well as maximal triangulable subalgebras of restricted Cartan type Lie algebras of type W, S and H. We are particularly interested in maximal
Ke Ou, Bin Shu
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On spherical ideals of Borel subalgebras
Archiv der Mathematik, 2005Let \(G\) 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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Varieties of Borel subalgebras for the Jacobson–Witt Lie algebras
Forum Mathematicum, 2023AbstractLetW(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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Borel Subalgebras of Schur Superalgebras
Algebra and Logic, 2005Summary: 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 ...
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Exact borel subalgebras of quasi-hereditary algebras. II
Communications in Algebra, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Conjugation-uniqueness of exact Borel subalgebras
Science in China Series A: Mathematics, 1999Exact 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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Algebraic Lie algebras with complete Borel subalgebras
Linear and Multilinear Algebra, 2009In 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, Xuansheng Wang
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EULER EQUATIONS ON BOREL SUBALGEBRAS OF SEMISIMPLE LIE ALGEBRAS
Mathematics of the USSR-Izvestiya, 1980A method connected with the translates of the invariants and semi-invariants of Ad* is given for the construction of completely integrable dynamical systems on real forms of Borel subalgebras of semisimple complex Lie algebras. A reduction of the noncommutative Liouville theorem to the commutative case is thereby obtained for the indicated class of Lie
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All quasihereditary algebras with a regular exact Borel subalgebra
Advances in Mathematics, 2021TERESA Conde
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