arXiv subjects

Nils Nornes

Publications and source records attributed to Nils Nornes.

2 recordsLinked to original sources

arXiv2015

Module Degenerations and Finite Field Extensions

Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a field, $K$ a finite extension of $k$ and $Λ$ a $k$-algebra. Then any $K\otimes_kΛ$-module is also a $Λ$-module. We study how the isomorphism classes, degeneration and hom-order differ depending on which algebra we are working over.

math.RT↗

arXiv2014

Degenerations of submodules and composition series

Let $M$ and $N$ be modules over an artin algebra such that $M$ degenerates to $N$. We show that any submodule of $M$ degenerates to a submodule of $N$. This suggests that a composition series of $M$ will in some sense degenerate to a composition series of $N$. We then study a subvariety of the module variety, consisting of those representations where all matrices are upper triangular. We show that these representations can be seen as representations of composition series, and that the orbit closures describe the above mentioned degeneration of composition series.

math.RT↗