In this paper we study irreducible representations of regular limit subalgebras of AF-algebras. The main result is twofold: every closed prime ideal of a limit of direct sums of nest algebras (NSAF) is primitive, and every prime regular limit algebra is primitive. A key step is that the quotient of a NSAF algebra by any closed ideal has an AF C*-envelope, and this algebra is exhibited as a quot...

We study simply connected Lie groups $G$ for which the hull-kernel topology of primitive ideal space $\text{Prim}(G)$ group $C^*$-algebra $C^*(G)$ is $T_1$, that is, finite subsets are closed. Thus, we prove AF-embeddable. To this end, show if solvable and its action on centre $[G, G]$ has at least one imaginary weight, then no nonempty quasi-compact open subsets. in addition locally compact wi...

Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a prim...

Let SI be a finite dimensional algebra with unit element over a field. 21 is generalized uniserial if every primitive (left or right) ideal has a unique composition series. 21 is a UMFR algebra (an algebra with a unique minimal faithful representation) if 21 has only one faithful representation which is minimal with respect to being faithful. The notation used in this paper will be that of an e...

Motivation • Cryptographic constructions based on lower-level primitives are often analyzed by modeling the primitive as an ideal object – Sometimes, impossible to construct based on standard assumptions – Here: hash functions from block ciphers • When instantiated, the primitive may have " defects " and be far from ideal Motivating example • Related-key attacks on block ciphers – Several such ...