Discriminants and Jacobians of virtual reflection groups

Details Discriminants and Jacobians of virtual reflection groups Discriminants and Jacobians of virtual reflection groups

2010-01-25

arxiv.org/abs/1001.4470v3

Mathematics

Group Theory

Version 3: 12 pages, corrected typos, updated references

Scientific paper

Let A be a polynomial algebra with complex coefficients. Let B be a finite extension ring of A which is also a polynomial algebra. We describe the factorisation of the Jacobian J of the extension into irreducibles. We also introduce the notion of a well-ramified extension and define its discriminant polynomial D. In the particular case where A is the ring of invariants of B under the action of a group (i.e., a Galois extension), this framework corresponds to the classical invariant theory of complex reflection groups. In the more general case of a well-ramified extension, we explain how the pair (D,J) behaves similarly to a Galois extension. This work can be viewed as the first step towards a possible invariant theory of "virtual reflection groups".

Affiliated with

Also associated with

No associations

Rating

Discriminants and Jacobians of virtual reflection groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Discriminants and Jacobians of virtual reflection groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discriminants and Jacobians of virtual reflection groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131309