Results 21 to 30 of about 405 (171)

A note on q-oscillator realizations of Uq(gl(M|N)) for Baxter Q-operators

Nuclear Physics B, 2019
We consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra Uq(gl(M|N)), and obtain q-oscillator realizations of the contracted algebras proposed in [1]. Instead of factoring out the invariant
Zengo Tsuboi
doaj   +1 more source

From quasi‐hereditary algebras with exact Borel subalgebras to directed bocses [PDF]

, 2020
Up to Morita equivalence, every quasi-hereditary algebra is the dual algebra of a directed bocs or coring. From the bocs, an exact Borel subalgebra is obtained.
Tomasz Brzezinski, Koenig, Steffen,, Külshammer, Julian,, Brzezinski, Tomasz,   +3 more
core   +1 more source

Polynomial Relations for q-Characters via the ODE/IM Correspondence

Symmetry, Integrability and Geometry: Methods and Applications, 2012
Let $U_q(mathfrak{b})$ be the Borel subalgebra of a quantum affine algebra of type $X^{(1)}_n$ ($X=A,B,C,D$). Guided by the ODE/IM correspondence in quantum integrable models, we propose conjectural polynomial relations among the $q$-characters of ...
Juanjuan Sun
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

Ad-nilpotent ideals of a parabolic subalgebra

, 2008
We extend the results of Cellini and Papi [P. Cellini, P. Papi, Ad-nilpotent ideals of a Borel subalgebra, J. Algebra 225 (2000) 130–140; P. Cellini, P. Papi, Ad-nilpotent ideals of a Borel subalgebra II, J.
Righi, Céline
core   +1 more source

A Non-commutative *-algebra of Borel Functions

, 2012
To the pair (E,c), where E is a countable Borel equivalence relation on a standard Borel space (X,A) and c a normalized Borel T-valued 2-cocycle on E, we associate a sequentially weakly closed Borel *-algebra Br*(E,c), contained in the bounded linear ...
Hart, Robert
core   +2 more sources

Uniqueness of Exact Borel Subalgebras and Bocses

Memoirs of the American Mathematical Society
In 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

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, Cheuk Yu Mak, Dan Pomerleano   +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

Abelian ideals in a Borel subalgebra of a complex simple Lie algebra [PDF]

, 2018
Let $\mathfrak{g}$ be a complex simple Lie algebra and $\mathfrak{b}$ a fixed Borel subalgebra of $\mathfrak{g}$ . We describe the abelian ideals in $\mathfrak{b}$ in a uniform way, that is, independent of the classification of complex simple Lie ...
Suter, Ruedi
core