The relative hermitian picard group

Sánchez, M. V. Reyes; Verhaeghe, Paul; Verschoren, A.

doi:10.1080/00927879508825439

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“…C and D will be involutive k-coalgebras, with involutions wc and w o . We want to thank Beatriz Abadie, Marivi Reyes Sanchez and Peter Verhaeghe, for discussions and comments on [I], [8] and [ll].…”

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confidence: 99%

On the picard group of involutive algebras and coalgebras

Farinati¹,

Solotar²

1998

Communications in Algebra

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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 clansical 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 coalgebraa (C, w c ) , which show, at least in the cocommutative case, that this hermitian Picard group differs considerably from the non hermitian one. Contents 1 I n t r o d u c t i o n 3 H e r m i t i a n M o r i t a t h e o r y 3 A l g e b r a i c H i l b e r t b i m o d u l e s a n d t h e h e r m i t i a n P i c a r d g r o u p 4 T h e h e r m i t i a n P i c a r d g r o u p o f a n involutive c o a l g e b r a

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confidence: 99%