We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.
It is well known that, given an endofunctor on a category , the initial -algebras (if existing), i.e., the algebras of (wellfounded) -terms over different variable supplies , give rise to a monad with substitution as the extension operation (the free monad induced by the functor ). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness),...
It is well known that, given an endofunctor H on a category C , the initial (A+H-)-algebras (if existing), i.e. , the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [12] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete...