Free Extensions and Jordan type
Abstract
Free extensions of commutative Artinian algebras were introduced by T. Harima and J. Watanabe. The Jordan type of a multiplication map $m$ by a nilpotent element of an Artinian algebra is the partition determining the sizes of the blocks in a Jordan matrix for $m$. We show that a free extension of the Artinian algebra $A$ with fibre $B$ is a deformation of the usual tensor product. This has consequences for the generic Jordan types of $A,B$ and $C$, showing that the Jordan type of $C$ is at least that of the usual tensor product in the dominance order. We give applications to algebras of relative coinvariants of linear group actions on a polynomial ring.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.02767
- arXiv:
- arXiv:1806.02767
- Bibcode:
- 2018arXiv180602767I
- Keywords:
-
- Mathematics - Commutative Algebra;
- 13E10 (Primary);
- 13A50;
- 13D40;
- 13H10;
- 14B07;
- 14C05
- E-Print:
- v3 17p. Has clarification of free extension as deformation of tensor product, after referee comment