Two questions on stable equivalences of Morita type
Yuming Liu, Guodong Zhou, Alexander Zimmermann
TL;DR
This paper investigates the properties of stable equivalences of Morita type, demonstrating that they do not preserve tensor products or trivial extensions, contrary to what is known for derived equivalences.
Contribution
It provides the first counterexamples showing that stable equivalences of Morita type do not preserve tensor products or trivial extensions.
Findings
Stable equivalences of Morita type do not preserve tensor products.
Stable equivalences of Morita type do not preserve trivial extensions.
Contrasts with properties preserved by derived equivalences.
Abstract
It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra