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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A locally compact group $G$ is said to be $\ast$-regular if the natural map$\Psi:\Prim C^\ast(G)\to\Prim_{\ast} L^1(G)$ is a homeomorphism with respect tothe Jacobson topologies on the primitive ideal spaces $\Prim C^\ast(G)$ and$\Prim_{\ast} L^1(G)$. In 1980 J. Boidol characterized the $\ast$-regular onesamong all exponential Lie groups by a purely algebraic condition. In thisarticle we introduce the notion of $L^1$-determined ideals in order to discussthe weaker property of primitive $\ast$-regularity. We give two sufficientcriteria for closed ideals $I$ of $C^\ast(G)$ to be $L^1$-determined. Herefromwe deduce a strategy to prove that a given exponential Lie group is primitive$\ast$-regular. The author proved in his thesis that all exponential Lie groupsof dimension $\le 7$ have this property. So far no counter-example is known.Here we discuss the example $G=B_5$, the only critical one in dimension $\le5$.

L1-determined ideals in group algebras of exponential Lie groups