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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 (C,ωC), which show, at least in the cocommutative case, that this hermitian Picard group differs considerably from the non hermitian one.

Registro:

Documento: Artículo
Título:On the Picard group of involutive algebras and coalgebras
Autor:Farinati, M.A.; Solotar, A.
Filiación:Depto. de Matemática, Fac. de Cs. Exactas y Naturales, Ciudad Universitaria Pab I, 1428, Buenos Aires, Argentina
Año:1998
Volumen:26
Número:7
Página de inicio:2115
Página de fin:2137
DOI: http://dx.doi.org/10.1080/00927879808826264
Título revista:Communications in Algebra
Título revista abreviado:Commun. Algebra
ISSN:00927872
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v26_n7_p2115_Farinati

Referencias:

  • Abadie, B., Exel, R., Hilbert C*-bimodules over commutative C* -algebras and an isomorphism condition for quantum Heisenberg manifolds (1997) Rev. Math.Phys., 9 (4), pp. 411-423
  • Cohen, M., A Morita context related to finite automorphism groups of rings (1985) Pacific J. Algebra, 95, pp. 153-172
  • Farinati, M.A., Solotar, A.L., Morita equivalence for positive Hochschild homology and dihedral homology (1996) Comm. in Alg., 24 (5), pp. 1793-1807
  • Farinati, M.A., Solotar, A.L., Morita - Takeuchi equivalence, cohomology of coalgebras and Azumaya coalgebras Lecture Notes Series, , To appeal in "Rings, Hopf algebras and Brauer groups", Ed. Marcel Dekker
  • Frölich, A., The Picard group of commutative rings (1973) Trans. A.M.S., 180, pp. 1-32
  • Hahn, A., An hermitian Morita theorem for algebras with antistructure (1985) J.of Alg., 93, pp. 215-235
  • Morita, K., Duality of modules and its applications to the theory of rings with minimium condition (1958) Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 6, pp. 85-142
  • Reyes Sanchez, M.V., Verhaeghe, P., Verschoren, A., The Relative Hermitian Picard Group (1995) Comm. in Alg., 23 (10), pp. 3915-3941
  • Takeuchi, M., Morita theorems for categories of comodules (1977) J. Fac. Sci. Univ. Tokyo., 24, pp. 1483-1528
  • Torrecillas, B., Zhang, Y.H., The Picard group of coalgebras (1996) Comm. in Alg., 24 (7), pp. 2235-2247
  • Verhaeghe, P., (1996) Hermitian Morita Theory, , Thesis. Univeisiteit Antwerpen

Citas:

---------- APA ----------
Farinati, M.A. & Solotar, A. (1998) . On the Picard group of involutive algebras and coalgebras. Communications in Algebra, 26(7), 2115-2137.
http://dx.doi.org/10.1080/00927879808826264
---------- CHICAGO ----------
Farinati, M.A., Solotar, A. "On the Picard group of involutive algebras and coalgebras" . Communications in Algebra 26, no. 7 (1998) : 2115-2137.
http://dx.doi.org/10.1080/00927879808826264
---------- MLA ----------
Farinati, M.A., Solotar, A. "On the Picard group of involutive algebras and coalgebras" . Communications in Algebra, vol. 26, no. 7, 1998, pp. 2115-2137.
http://dx.doi.org/10.1080/00927879808826264
---------- VANCOUVER ----------
Farinati, M.A., Solotar, A. On the Picard group of involutive algebras and coalgebras. Commun. Algebra. 1998;26(7):2115-2137.
http://dx.doi.org/10.1080/00927879808826264