Severi-Brauer varieties of semidirect product algebras.
The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements...
In questo lavoro studiamo i non CC-gruppi monolitici con tutti i quozienti propri CC-gruppi, che hanno sottogruppi abeliani normali non banali.
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .
Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and -free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic...
Assume that K is an arbitrary field. Let (I,⪯) be a poset of finite prinjective type and let KI be the incidence K-algebra of I. A classification of all sincere posets of finite prinjective type with three maximal elements is given in Theorem 2.1. A complete list of such posets consisting of 90 diagrams is presented in Tables 2.2. Moreover, given any sincere poset I of finite prinjective type with three maximal elements, a complete set of pairwise non-isomorphic sincere indecomposable prinjective...
Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .