By improving the previous construction in [18] we observe that any reduced HNN extension is a corner of a certain reduced amalgamated free product in both the von Neumann algebra and the C∗-algebra settings. Then, the same fact is shown for universal HNN extensions of C∗-algebras. We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann ...

Recent investigations of lax algebras—in generalization of Barr’s relational algebras—make an essential use of lax extensions of monad functors on Set to the category Rel(V) of sets and V-relations (where V is a unital quantale). For a given monad there may be many such lax extensions, and different constructions appear in the literature. The aim of this article is to shed a unifying light on t...

We describe all central extensions of $3$-dimensional non-zero complex Zinbiel algebras. As a corollary, we have full classification $4$-dimensional non-trivial algebras and $5$-dimensional with $2$-dimensional annihilator, which gives the principal step in algebraic