Abstract
We introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The Gabriel quiver of such an algebra is the triangulation quiver associated to the coherent orientation of the tetrahedron. Surprisingly, these algebras occurred in the classification of all algebras of generalized quaternion type, but are not weighted surface algebras. We prove that a higher tetrahedral algebra is periodic if and only if it is non-singular.
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The research was done during the visit of the first named author at the Faculty of Mathematics and Computer Sciences in Toruń (June 2017).
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Presented by Jon F. Carlson.
The research was supported by the research grant DEC-2011/02/A/ST1/00216 of the National Science Center Poland.
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Erdmann, K., Skowroński, A. Higher Tetrahedral Algebras. Algebr Represent Theor 22, 387–406 (2019). https://doi.org/10.1007/s10468-018-9772-x
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DOI: https://doi.org/10.1007/s10468-018-9772-x