Publication
Title
Hereditary coalgebras
Author
Abstract
In this note, we study the global dimension of coalgebras and discuss the class of coalgebras of global dimension less or equal to 1. The coalgebras in this class, which contains all the cosemisimple coalgebras, are called hereditary coalgebras. If C is a finite dimensional coalgebra, then C is hereditary if and only if C* (the convolution algebra of C) is a hereditary algebra. Any direct sum of hereditary coalgebras is hereditary too. This gives us many examples of infinite dimensional hereditary coalgebras. A coalgebra is left hereditary if and only if it is right hereditary. Moreover, there do not exist hereditary Hopf algebras of finite dimension which are not cosemisimple.
Language
English
Source (journal)
Communications in algebra. - New York, N.Y.
Publication
New York, N.Y. : 1996
ISSN
0092-7872
Volume/pages
24:4, p. 1521-1528
ISI
A1996UC85200019
Full text (Publisher's DOI)
UAntwerpen
Publication type
Subject
External links
Web of Science
Record
Identification
Creation 29.02.2012
Last edited 19.08.2017