Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-16T10:27:30.313Z Has data issue: false hasContentIssue false

Chapter 7 - Examples of bimonoids

from Part II - Basic theory of bimonoids

Published online by Cambridge University Press:  28 February 2020

Marcelo Aguiar
Affiliation:
Cornell University, Ithaca
Swapneel Mahajan
Affiliation:
Indian Institute of Technology, Mumbai
Get access

Summary

We discuss some basic and important examples of species (relative to a fixed hyperplane arrangement). These include the exponential species, signed exponential species, species of chambers, species of faces, species of flats, species of top-nested faces, species of top-lunes, species of bifaces. They are constructed from well-known objects associated to an arrangement such as faces, flats, chambers, top-nested faces, top-lunes, bifaces. The exponential species is simpler and has all its components equal to the base field. Each of these species carries the structure of a bimonoid. Some of them also admit q-analogues. All these bimonoids arise from universal constructions. We also introduce the Lie species and Zie species. These arise as the primitive part of the bimonoids of chambers and faces, respectively. As a consequence, they carry the structure of a Lie monoid.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×