
TL;DR
This paper investigates the classification problem of multi-graded nilpotent tuples, generalizing graded nilpotent pairs, by analyzing their shapes and representation types through multi-staircase algebras.
Contribution
It introduces the concept of multi-graded nilpotent tuples, defines their shapes, and classifies their representation types using multi-staircase algebras.
Findings
Classification of representation types for multi-staircase algebras
Determination of finiteness conditions for multi-graded nilpotent tuples
Extension of nilpotent pair theory to multi-graded settings
Abstract
We discuss multi-graded nilpotent tuples of multi-graded vector spaces which are a generalization of graded nilpotent pairs. The multi-grading yields a natural notion of a shape of such tuple and our main interest is to answer the question "Is the number of multi-graded nilpotent tuples of a fixed shape, up to base change in the homogeneous components, finite?" Our methods make use of a translation to the class of so-called "Multi-staircase algebras" and we classify their representation types.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
