On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds

• Autorzy: José Isidro
• Języki publikacji: EN

Abstrakty

EN

The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.

Słowa kluczowe

EN

Classical symmetric complex Banach manifolds; JB*-triples; Cartan factors; Banach-Lie algebras; Complete holomorphic vector fields

Kategorie tematyczne

• 17B65: Infinite-dimensional Lie (super)algebras
• 17C65: Jordan structures on Banach spaces and algebras
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties
• 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 4
• Strony: 696-709

Daty

wydano

2007-12-01

online

2007-12-01

Twórcy

autor

José Isidro

• Santiago de Compostela

Bibliografia

• [1] T.J. Barton and Y. Friedman: “Bounded derivations of JB*-triples”, Quart. J. Math. Oxford Ser. 2, Vol. 41, (1990), pp. 255–268. http://dx.doi.org/10.1093/qmath/41.3.255
• [2] D. Beltită and M. Sabac: Lie algebras of bounded operators, Operator Theory: Advances and Applications, Vol. 120, Birkhäuser Verlag, Basel, 2001.
• [3] P. Civin and B. Yood: “Lie and Jordan structures in Banach algebras”, Pacific J. Math., Vol. 15, (1965), pp. 775–797.
• [4] J.B. Conway: A course in operator theory, Graduate Studies in Mathematics, Vol. 21, American Mathematical Society, Providence RI, 2000.
• [5] S. Dineen and R.M. Timoney: “The centroid of a JB*-triple system”, Math. Scand., Vol. 62, (1988), pp. 327–342.
• [6] C.K. Fong, C.R. Miers and A.R. Sourour: “Lie and Jordan ideals of operators on Hilbert space”, Proc. Amer. Math. Soc., Vol. 84, (1982), pp. 516–520. http://dx.doi.org/10.2307/2044026
• [7] C.K. Fong and G.J. Murphy: “Ideals and Lie ideals of operators”, Acta Sci. Math., Vol. 51, (1987), pp. 441–456.
• [8] L.A. Harris: “Bounded symmetric homogeneous domains in infinite dimensional spaces”, Proceedings on Infinite Dimensional Holomorphy, Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973, pp. 13–40, Lecture Notes in Math., Vol. 364, Springer, Berlin, 1974. http://dx.doi.org/10.1007/BFb0069002
• [9] F.J. Hervés and J.M. Isidro: “Isometries and automorphisms of the spaces of spinors”, Rev. Mat. Univ. Complut. Madrid, Vol. 5, (1992), pp. 193–200.
• [10] T. Ho, J. Martinez-Moreno, A.M. Peralta and B. Russo: “Derivations on real and complex JB*-triples”, J. London. Math. Soc.(2), Vol. 65, (2002), pp. 85–102. http://dx.doi.org/10.1112/S002461070100271X
• [11] J.M. Isidro and W. Kaup: “Weak continuity of holomorphic automorphisms in JB*-triples”, Math. Z., Vol. 210, (1992), pp. 277–288. http://dx.doi.org/10.1007/BF02571798
• [12] W. Kaup: “On real Cartan factors”, Manuscripta Math., Vol. 92, (1997), pp. 191–222. http://dx.doi.org/10.1007/BF02678189
• [13] M. Koecher: “Imbedding of Jordan algebras into Lie algebras I”, Amer. J. Math., Vol. 89, (1967), pp. 787–816. http://dx.doi.org/10.2307/2373242
• [14] M. Koecher: “Imbedding of Jordan algebras into Lie algebras II”, Amer. J. Math., Vol. 90, (1968), pp. 476–510. http://dx.doi.org/10.2307/2373540
• [15] O. Loos: Bounded symmetric domains and Jordan pairs, University of California at Irvine, Lecture Notes, 1997.
• [16] K. Meyberg: “Jordan-Triplesysteme und die Koecher-Konstruktion von Lie-Algebren”, Math. Z., Vol. 115, (1970), pp. 58–78. http://dx.doi.org/10.1007/BF01109749
• [17] K. Meyberg: “Zur Konstruktion von Lie-Algebren aus Jordan-Triplesystemen”, Manuscripta Math., Vol. 3, (1970), pp. 115–132. http://dx.doi.org/10.1007/BF01273306
• [18] C.R. Miers: “Closed Lie ideals in operator algebras”, Canad. J. Math., Vol. 33, (1981), pp. 1271–1278.
• [19] D.M. Topping: “On linear combinations of special operators”, J. Algebra, Vol. 10, (1968), pp. 516–521. http://dx.doi.org/10.1016/0021-8693(68)90077-X
• [20] H. Upmeier: Symmetric Banach manifolds and Jordan C*-algebras, North Holland Mathematics Studies, Vol. 104, North-Holland Publishing Co., Amsterdam, 1985.

Identyfikatory

DOI

10.2478/s11533-007-0028-y