Abstract
Based on the fact that the relatively stable category of a p-block B is equivalent to the relatively stable category of its Brauer correspondent b as triangulated category, we introduce the notion of relatively stable equivalence of Morita type and show that there is a relatively stable equivalence of Morita type between B and b. Some invariants under stable equivalence of Morita type can be generalized to this relative case. In particular, we put forward the generalized Alperin–Auslander conjecture and prove it in special cases.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.