Title
Hereditary coalgebras Hereditary coalgebras
Author
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Communications in algebra. - New York, N.Y.
Volume/pages
24() :4 , p. 1521-1528
ISSN
0092-7872
ISI
A1996UC85200019
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
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.
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