Results 21 to 30 of about 285 (163)
Induced Modules for Affine Lie Algebras
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P ...
Vyacheslav Futorny, Iryna Kashuba
doaj +1 more source
Abelian Ideals with Given Dimension in Borel Subalgebras [PDF]
Algebra Colloquium, 2012 A well-known Peterson's theorem says that the number of abelian ideals in a Borel subalgebra of a rank-r finite-dimensional simple Lie algebra is exactly 2r. In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra of finite-dimensional simple Lie algebras, which is a refinement of Peterson's theorem capturing ...
openaire +2 more sources
SciPost Physics CoreWe consider the cyclic representations $\Omega_{rs}$ of $U_q(\widehat{\mathfrak{sl}}_2)$ at $q^N=1$ that depend upon two points $r,s$ in the chiral Potts algebraic curve. We show how $\Omega_{rs}$ is related to the tensor product $\rho_r\otimes \bar{\rho}
Robert Weston
doaj +1 more source
Uniqueness of Exact Borel Subalgebras and Bocses
Memoirs of the American Mathematical SocietyIn the article by König, Külshammer, and Ovsienko (Adv. Math 262 (2014), 546–592), together with Koenig and Ovsienko, the first author showed that every quasi-hereditary algebra can be obtained as the (left or right) dual of a directed bocs.
Kuelshammer, Julian, Miemietz, Vanessa
openaire +2 more sources
Abelian Ideals of a Borel Subalgebra and Root Systems, II [PDF]
Algebras and Representation Theory, 2019 12 ...
openaire +3 more sources
Coulomb branch algebras via symplectic cohomology
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract Let (M¯,ω)$(\bar{M}, \omega)$ be a compact symplectic manifold with convex boundary and c1(TM¯)=0$c_1(T\bar{M})=0$. Suppose that (M¯,ω)$(\bar{M}, \omega)$ is equipped with a convex Hamiltonian G$G$‐action for some connected, compact Lie group G$G$.
Eduardo González +2 more
wiley +1 more source
A note on relative Gelfand–Fuks cohomology of spheres
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We study the Gelfand–Fuks cohomology of smooth vector fields on Sd$\mathbb {S}^d$ relative to SO(d+1)$\mathrm{SO}(d+1)$ following a method of Haefliger that uses tools from rational homotopy theory. In particular, we show that H∗(BSO(4);R)$H^*(\mathrm{B}\mathrm{SO}(4);\mathbb {R})$ injects into the relative Gelfand–Fuks cohomology which ...
Nils Prigge
wiley +1 more source
On the Conjugacy Theorems of Cartan and Borel Subalgebras [PDF]
, 2010 We study the conjugacy theorems of Cartan subalgebras and Borel subalgebras of general Lie algebras. We present a history of the problem, along with two proofs of the theorems which stay completely within the realm of Lie algebras.
Thompson, Mary Clair
core
Algebraic singular functions are not always dense in the ideal of C∗$C^*$‐singular functions
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We give the first examples of étale (non‐Hausdorff) groupoids G$\mathcal {G}$ whose C∗$C^*$‐algebras contain singular elements that cannot be approximated by singular elements in Cc(G)$\mathcal {C}_c(\mathcal {G})$. We provide two examples: one is a bundle of groups and the other a minimal and effective groupoid constructed from a self‐similar
Diego Martínez, Nóra Szakács
wiley +1 more source
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We count and give a parametrization of connected components in the space of flags transverse to a given transverse pair in every flag varieties of SO0(p,q)$\operatorname{SO}_0(p,q)$. We compute the effect the involution of the unipotent radical has on those components and, using methods of Dey–Greenberg–Riestenberg, we show that for certain ...
Clarence Kineider, Roméo Troubat
wiley +1 more source