Invariants of coalgebras (Q2738451)

The Picard group of a coalgebra was introduced by \textit{Y. H. Zhang} and the reviewer [in Commun. Algebra 24, No. 7, 2235-2247 (1996; Zbl 0863.16034)] and the Brauer group by the same authors and \textit{F. Van Oystaeyen} [in J. Algebra 177, No. 2, 536-568 (1995; Zbl 0837.16037)], these are two basic invariants that are considered in this semi-survey paper. The authors also include some new results and examples in this theory, thus it is shown that if \(C\) is a cocommutative irreducible coalgebra, the group homomorphism \((-)^*\colon\text{Br}(C)\to\text{Br}(C^*)\), \([A]\mapsto[A^*]\) is injective. In the last section, the Schur group of a coalgebra is investigated.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00025].