On the picard group of involutive algebras and coalgebras

Abstract

We study how Hilbert bimodules correspond in the algebraic case to hermitian Morita equivalences and consequently we obtain a description of the hermitian Picard group of a commutative involutive algebra A as the semidirect product of the classical hermitian Picard group of A and the automorphisms of A commuting with the involution. We also obtain similar decomposition results on hermitian Picard groups of involutive coalgebras (Cω_c), which show, at least in the cocommutative case, that this hermitian Picard group differs considerably from the non hermitian one.

¹Research supported by UBACYT EX230, CONICET-PIA 6213/96 and Fundatión Antorchas.

¹Research supported by UBACYT EX230, CONICET-PIA 6213/96 and Fundatión Antorchas.

Notes

¹Research supported by UBACYT EX230, CONICET-PIA 6213/96 and Fundatión Antorchas.