O'Farrell, Anthony G. and Zaitsev, Dmitri
(2014)
Factoring Formal Maps into Reversible or Involutive Factors.
Journal of Algebra, 399.
pp. 657-674.
ISSN 0021-8693
Abstract
An element g of a group is called reversible if it is conjugate in the group to its inverse.
An element is an involution if it is equal to its inverse. This paper is about factoring elements as
products of reversibles in the group Gn of formal maps of (Cn, 0), i.e. formally-invertible n-tuples
of formal power series in n variables, with complex coefficients. The case n = 1 was already
understood [25].
Each product F of reversibles has linear part L(F) of determinant ±1. The main results are
that for n ≥ 2 each map F with det(L(F)) = ±1 is the product of 2+3 • ceiling(log2 n) reversibles,
and may also be factored as the product of 9 + 6 • ceiling(log2 n) involutions (where the ceiling of
x is the smallest integer ≥ x).
| Item Type: |
Article
|
| Additional Information: |
This is the preprint version of the published article, which is available at doi:10.1016/j.jalgebra.2013.09.053 |
| Keywords: |
Involution; Reversible; Power series; Group; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: |
6271 |
| Identification Number: |
https://doi.org/10.1016/j.jalgebra.2013.09.053 |
| Depositing User: |
Prof. Anthony O'Farrell
|
| Date Deposited: |
17 Jul 2015 14:51 |
| Journal or Publication Title: |
Journal of Algebra |
| Publisher: |
Elsevier |
| Refereed: |
Yes |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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