Results 1 to 10 of about 135 (125)
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.
Simon Lentner, Lentner Simon
exaly +3 more sources
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.
exaly +2 more sources
Local and 2-Local Derivations of Locally Simple Lie Algebras
Современная математика: Фундаментальные направления, 2022 In the present paper, we study local and 2-local derivations of the classical locally simple Lie algebras. Firstly, we prove that every local and 2-local derivations on classical locally simple Lie algebra is a derivation.
Sh. A. Ayupov +2 more
doaj +1 more source
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 +2 more
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
The Bruhat order on abelian ideals of Borel subalgebras [PDF]
Transactions of the American Mathematical Society, 2020 Let G G be a quasi-simple algebraic group over an algebraically closed field
Gandini, Jacopo +3 more
openaire +5 more sources
Cohomology of nilradicals of Borel subalgebras [PDF]
Transactions of the American Mathematical Society, 1974 Let 9? be the maximal nilpotent ideal in a Borel subalgebra of a complex simple Lie algebra. The cohomology groups HA91, 9M), H11(91. *) and the 9N-invariant symmetric bilinear forms on 91 are determined. The main result is the computation of H2(1,9).
Leger, George F., Luks, Eugene M.
openaire +2 more sources
Borel Type Subalgebras of theq-SchurmAlgebra
Journal of Algebra, 1999 Jie Du, Hebing Rui
exaly +2 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, PAPI, Paolo
openaire +2 more sources
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"
PAPI, Paolo, CELLINI P.
openaire +5 more sources