Results 61 to 70 of about 405 (171)
Modular representations of the Yangian Y2$Y_2$
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Let Y2$Y_2$ be the Yangian associated to the general linear Lie algebra gl2$\mathfrak {gl}_2$, defined over an algebraically closed field k$\mathbb {k}$ of characteristic p>0$p>0$. In this paper, we study the representation theory of the restricted Yangian Y2[p]$Y^{[p]}_2$.
Hao Chang, Jinxin Hu, Lewis Topley
wiley +1 more source
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, some properties of weighted Segal algebras are investigated. The condition under which it guarantees the existence of a central approximate identity for weighted Segal algebras is given. Also, various homological and cohomological properties of weighted Segal algebras are obtained.
Batoul S. Mortazavi-Samarin +3 more
wiley +1 more source
Quasi-hereditary algebras, exact Borel subalgebras, A∞-categories and boxes
, 2014 Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category O.
Ovsienko, Sergiy, +2 more
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Nilpotent subspaces of maximal dimension in semisimple Lie algebras [PDF]
, 2006 We show that a linear subspace of a reductive Lie algebra g that consists of nilpotent elements has dimension at most equal to the number of positive roots, and that any nilpotent subspace attaining this upper bound is equal to the nilradical of a Borel ...
Kuttler, J +8 more
core +1 more source
Verma modules induced from nonstandard Borel subalgebras [PDF]
Pacific Journal of Mathematics, 1994 Let \(A\) be an indecomposable generalized Cartan matrix of affine type and \({\mathfrak g} (A)\) the corresponding affine Kac-Moody algebra. Unlike finite-dimensional semisimple Lie algebras, \({\mathfrak g} (A)\) admits several conjugacy classes of Borel subalgebras (or equivalently several nonconjugate choices of positive roots).
openaire +2 more sources
Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3634-3642, December 2024.Abstract We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank‐one totally geodesic subspaces. Among the consequences, we prove the existence of a nonconstant, globally defined complex‐valued harmonic morphism from the Riemannian symmetric space associated to a split real semisimple ...
F. E. Burstall
wiley +1 more source
Exact Borel subalgebras of path algebras of quivers of Dynkin type $\mathbb{A}$
, 2023 Hereditary algebras are quasi-hereditary with respect to any adapted partial order on the indexing set of the isomorphism classes of their simple modules.
Thuresson, Markus
core
Nilpotent subalgebras of semisimple Lie algebras [PDF]
, 2009 Let g be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of g consisting of nilpotent elements is contained in some Borel subalgebra.
Levy, Paul +6 more
core +1 more source
Irreducible modules for the quantum affine algebra Uq(g) and its Borel subalgebra Uq(g)⩾0
, 2007 Let g be an affine Kac–Moody Lie algebra, and let Uq(g) be its quantized universal enveloping algebra. Let the Borel subalgebra Uq(g)⩾0 of Uq(g) be the nonnegative part of Uq(g) with respect to the standard triangular decomposition.
Bowman, John
core +1 more source
, 2022 We consider the string, like point particles and branes, to be an irreducible representation of the semi-direct product of the Cartan involution invariant subalgebra of E11 and its vector representation.
West, Peter, Glennon, Keith
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