English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For every associative algebra $A$ and every class $\mathcal{C}$ ofrepresentations of $A$ the following question (related to nullstellensatz)makes sense: Characterize all tuples of elements $a_1,\ldots,a_n \in A$ suchthat vectors $\pi(a_1)v,\ldots,\pi(a_n)v$ are linearly dependent for every $\pi\in \mathcal{C}$ and every $v$ from the representation space of $\pi$. Weanswer this question in the following cases:  (1) $A=U(L)$ is the enveloping algebra of a finite-dimensional complex Liealgebra $L$ and $\mathbb{C}$ is the class of all finite-dimensionalrepresentations of $A$.  (2) $A=U(\mathfrak{sl}_2(\mathbb{C}))$ and $\mathbb{C}$ is the class of allfinite-dimensional irreducible representations of $A$.  (3) $A=U(\mathfrak{sl}_3(\mathbb{C}))$ and $\mathbb{C}$ is the class of allfinite-dimensional irreducible representations of $A$ with sufficiently highweights.  In case (1) the answer is: tuples that are linearly dependent over$\mathbb{C}$ while in cases (2) and (3) the answer is: tuples that are linearlydependent over the center of $A$. Similar results have been proved before forfree algebras and Weyl algebras.

A local-global principle for linear dependence in enveloping algebras of Lie algebras