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Generalized canonical algebras and standard stable tubes

Andrzej Skowroński (2001)

Colloquium Mathematicae

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.

Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials

Justyna Kosakowska (2012)

Colloquium Mathematicae

We prove that the monoid of generic extensions of finite-dimensional nilpotent k[T]-modules is isomorphic to the monoid of partitions (with addition of partitions). This gives us a simple method for computing generic extensions, by addition of partitions. Moreover we give a combinatorial algorithm that calculates the constant terms of classical Hall polynomials.

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