Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-19
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
A locally finite category is defined as a category in which every arrow admits only finitely many different ways to be factorized by composable arrows.
The large algebra of such categories over some fields may be defined, and with it a group of invertible series (under multiplication).
For certain particular locally finite categories, a substitution operation, generalizing the usual substitution of formal power series, may be defined, and with it a group of reversible series (invertible under substitution).
Moreover, both groups are actually affine groups.
In this contribution, we introduce their coordinate Hopf algebras which are both free as commutative algebras.
The semidirect product structure obtained from the action of reversible series on invertible series by anti-automorphisms gives rise to an interaction at the level of their coordinate Hopf algebras under the form of a smash coproduct.
American Psychological Association (APA)
Poinsot, Laurent. 2013. Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category. Algebra،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-466677
Modern Language Association (MLA)
Poinsot, Laurent. Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category. Algebra No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-466677
American Medical Association (AMA)
Poinsot, Laurent. Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category. Algebra. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-466677
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-466677