Abstract
We begin now systematic study of automorphism actions of a locally compact group on a von Neumann algebra. For those readers who are unfamiliar with a locally compact group or unwilling to spend extra minute on the general theory of locally compact groups should assume that your group is simply the additive group R of real numbers or Z of integers. We will take these two groups for applications in the later chapters.
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Notes on Chapter X
T. Turumaru, Crossed products of operator algebras, Tôhku J. Math., 10 (1958), 355–365.
N. Suzuki, Crossed products of rings of operators, Tôhoku Math. J., 11 (1959), 113–124.
M. Nakamura and Z. Takeda, On some elementary properties of the crossed products of von Neumann algebras, Proc. Japan Acad., 34 (1958), 489–494. A Galois theory for finite factors, Proc. Japan Acad., 36 (1960), 258–260.
M. Nakamura and Z. Takeda, On the fundamental theorem of the Galois theory for finite factors, Proc. Japan Acad., 36 (1960), 313–318.
O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics I, Springer-Verlag (1979), xiv+519. II, ibid. (1981), xiii+505.
G. Zeller-Meier, Produit croisé d’une C* -algèbre par un groupe d’automorphismes, J. Math. Pure et Appl., 47 (1968), 102–239.
M. Takesaki, Covariant representations of C* -algebras and their automorphism groups, Acta Math., 119 (1967), 273–302.
G. W. Mackey, Induced representations of locally compact groups I, Ann. Math., 55 (1952), 101–139. Induced representation of locally compact groups II, The Frobenius reciprocity theorem, ibid., 58 (1953), 193–221.
M. Enock and J. M. Schwartz, Kac alagebras and duality of locally compact groups, Springer-Verlag (1992), x + 257.
H. Takai, On a duality for crossed products of C* -algebras, J. Funct. Anal., 19 (1975), 25–39.
T. Digernes, Poids duals sur un produit croise, C. R. Acad. Sci. Paris„ 278 (1974), 937–940.
T. Digernes, Dual weights and the commutant theorem for crossed products of W*-algebras, Thesis, UCLA, (1975).
U. Haagerup, On the dual weight for crossed products of von Neumann algebras I, Math. Scand., 43 (1978), 99–118. II ibid., 119–140.
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Takesaki, M. (2003). Crossed Products and Duality. In: Theory of Operator Algebras II. Encyclopaedia of Mathematical Sciences, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10451-4_5
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DOI: https://doi.org/10.1007/978-3-662-10451-4_5
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