Abstract
AbstractWe demonstrate how exact structures can be placed on the additive category of right operator modules over an operator algebra in order to discuss global dimension for operator algebras. The properties of the Haagerup tensor product play a decisive role in this.
Highlights
Among the most important operator space modules over C*-algebras are the Hilbert C*modules, the operator modules and the matrix normed modules
The main difference between the second and the third class lies in the kind of complete boundedness which is required of the bilinear mappings that give the module action
We focus on an appropriate definition of cohomological dimension and, in particular, answer a question raised by Helemskii [16] whether quantised global dimension zero is equivalent to AMS subject classification (2020): 46L07, 46M10, 46M18, 18G20, 18G50
Summary
Among the most important operator space modules over C*-algebras are the Hilbert C*modules, the operator modules and the matrix normed modules. Completely bounded bilinear mappings and the module operator space projective tensor product ⊗⌢ govern the class of matrix normed modules; for details, we refer to [6, Chapter 3]. Both these classes have been put to good use and found a range of interesting applications; we only mention the recent papers [4], [10] and [11], [12] as samples. We discuss similarities and differences between our preferred category, OMod∞, and mnMod∞, the category of matrix normed modules over an operator algebra
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
