A note I'm studying says its primitive ideals space is $\lbrace \lbrace 0 \rbrace, \mathcal{B}_0(\mathcal{H}) \rbrace $. I think it might be just $\lbrace \lbrace 0 \rbrace \rbrace $ so I'm somewhat confused now. Anyone please help clarify?

Take the 2-minute tour
×

MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

whydo you think the answer should be $\{\{0\}\}$. Is the confusion over the terms "ideal" or "primitive"?? – Matthew Daws Jul 22 '11 at 16:38`$A^\sim = \{ (a,t) : a\in A, t\in\mathbb C\}$`

. Then the irrep you need is $A^\sim\rightarrow\mathbb C; (a,t) \mapsto t$. This is a homomorphism, and has kernel $A$. It's irreducible, as, well, it's non-zero, and $\mathbb C$ is one-dimensional! So your argument is wrong when you claim "This again contradicts the irreducibility". – Matthew Daws Jul 25 '11 at 13:12