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- W4249902564 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." @default.
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- W4249902564 date "1996-01-01" @default.
- W4249902564 modified "2023-10-17" @default.
- W4249902564 title "Hereditary coalgebras" @default.
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- W4249902564 doi "https://doi.org/10.1080/00927879608825649" @default.
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