arXiv subjects

Eun-Hee Cho

Publications and source records attributed to Eun-Hee Cho.

2 recordsLinked to original sources

arXiv2016

Symmetric bilinear form on a Lie algebra

Let $\frak g$ be the finite dimensional simple Lie algebra associated to an indecomposable and symmetrizable generalized Cartan matrix $C=(a_{ij})_{n\times n}$ of finite type and let $\frak d$ be a finite dimensional Lie algebra related to a quantum group $D_{q,p^{-1}}(\frak g)$ obtained by Hodges, Levasseur and Toro \cite{HoLeT} by deforming the quantum group $U_q(\frak g)$. Here we see that $\frak d$ is a generalization of $\frak g$ and give a $\frak d$-invariant symmetric bilinear form on $\frak d$.

math.RA↗

arXiv2016

Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra

We observe \cite[Proposition 4.1]{LaLe} that Poisson polynomial extensions appear as semiclassical limits of a class of Ore extensions. As an application, a Poisson generalized Weyl algebra $A_1$ considered as a Poisson version of the quantum generalized Weyl algebra is constructed and its Poisson structures are studied. In particular, it is obtained a necessary and sufficient condition such that $A_1$ is Poisson simple and established that the Poisson endomorphisms of $A_1$ are Poisson analogues of the endomorphisms of the quantum generalized Weyl algebra.

math.RA↗