Examples of tilting-discrete symmetric algebras
Takuma Aihara
TL;DR
This paper provides various examples of tilting-discrete symmetric algebras, explores their properties, and discusses related conjectures and disconnectedness, advancing understanding in algebra representation theory.
Contribution
It introduces new examples of tilting-discrete symmetric algebras and counterexamples to existing conjectures, enriching the classification and properties of these algebras.
Findings
Identified examples of tilting-discrete symmetric algebras.
Counterexample to the conjecture on { au}-tilting finite symmetric algebras.
Discussed tilting-disconnectedness in symmetric algebras.
Abstract
We give several examples of tilting-discrete symmetric algebras; in particular, one explores which algebra has tilting-discrete trivial extension. We provide a counter example of the conjecture stating any {\tau} -tilting finite symmetric algebra is tiltingdiscrete. Also, we discuss the tilting-disconnectedness of symmetric algebras and give new examples of tilting-disconnected symmetric algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Topics in Algebra