Hereditary coalgebras

被引：62

作者：

Nastasescu, C

Torrecillas, B

Zhang, YH

机构：

[1] UNIV ALMERIA,DEPT ALGEBRA & ANAL,E-04071 ALMERIA,SPAIN

[2] UNIV ANTWERP,DEPT MATH,B-2610 WILRIJK,BELGIUM

来源：

COMMUNICATIONS IN ALGEBRA | 1996年 / 24卷 / 04期

关键词：

D O I：

10.1080/00927879608825649

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1521 / 1528

页数：8