Results 61 to 70 of about 285 (163)
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
core +1 more source
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
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
Cohomology Theorems for Borel-Like Solvable Lie Algebras in Arbitrary Characteristic
, 1972 This paper develops some techniques for the study of derivation algebras and cohomology groups of Lie algebras. We are especially concerned with solvable algebras over arbitrary fields with structural properties like those of the Borel subalgebras of ...
G. Leger, E. Luks
core +1 more source
SCAP-subalgebras of Lie algebras [PDF]
, 2016 summary:A subalgebra $H$ of a finite dimensional Lie algebra $L$ is said to be a $\rm SCAP$-subalgebra if there is a chief series $0=L_0\subset L_1\subset \ldots \subset L_t=L$ of $L$ such that for every $i=1,2,\ldots ,t$, we have $H+L_i=H+L_{i-1}$ or $H\
Chehrazi, Sara, Salemkar, Ali Reza
core +1 more source
Abelian Subalgebras in Z2-graded Lie Algebras; Partitions, Young Diagrams and Ballot Numbers [PDF]
, 2010 The dissertation is broken into two parts. Part I deals with the following problem: suppose $\g = \g_0 \oplus \g_1$ is a simple $\Z_2$-graded Lie algebra and let $\mathfrak{b}_0$ be a fixed Borel subalgebra of $\g_0$; describe and enumerate the abelian $\
Dolbin, Ronald Raymond
core
Categories O for Dynkin Borel Subalgebras of Root-Reductive Lie Algebras
, 2017 The purpose of my Ph.D. research is to define and study an analogue of the classical Bernstein-Gelfand-Gelfand (BGG) category O for the Lie algebra g, where g is one of the finitary, infinite-dimensional Lie algebras gl(∞,K), sl(∞,K), so(∞,K), and sp(∞,
Nampaisarn, Thanasin
core
Computing of the number of right coideal subalgebras of Uq(so2n+1)
, 2011 In this paper we complete the classification of right coideal subalgebras containing all grouplike elements for the multiparameter version of the quantum group Uq(so2n+1), qt≠1. It is known that every such subalgebra has a triangular decomposition U=U−HU+
Kharchenko, V.K. +5 more
core +1 more source
A class of II1 factors with many non conjugate Cartan subalgebras
, 2012 We construct a class of II1 factors M that admit unclassifiably many Cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of M is complete analytic, in particular non Borel.
Speelman, An +3 more
core +1 more source
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.
openaire +2 more sources