Lie -triple homomorphisms into von Neumann algebras
Author:
C. Robert Miers
Journal:
Proc. Amer. Math. Soc. 58 (1976), 169-172
MSC:
Primary 46L10
DOI:
https://doi.org/10.1090/S0002-9939-1976-0410406-9
MathSciNet review:
0410406
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Abstract | References | Similar Articles | Additional Information
Abstract: Let and
be associative
-algebras. A Lie
-triple homomorphism of
into
is a
-linear map
such that
![$\displaystyle \phi [[A,B],C] = [[\phi (A),\phi (B)],\phi (C)].$](images/img12.gif)



![$ [X,Y] = XY - YX.)$](images/img16.gif)






![$ [M,M]$](images/img23.gif)


![$ [M,M]$](images/img26.gif)
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- [3] C. R. Miers, Lie homomorphisms of operator algebras, Pacific J. Math. 38 (1971), 717-737. MR 46 #7918. MR 0308804 (46:7918)
- [4]
C. Pearcy and D. Topping, Commutators in certain II
-factors, J. Functional Analysis 3 (1969), 69-78. MR 39 #789. MR 0239432 (39:789)
- [5] H. Sunouchi, Infinite Lie rings, Tôhoku Math. J. (2) 8 (1956), 291-307. MR 0101262 (21:75)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1976-0410406-9
Keywords:
Lie -triple homomorphism,
von Neumann algebra
Article copyright:
© Copyright 1976
American Mathematical Society