The Number of Two-Term Tilting Complexes over Symmetric Algebras with Radical Cube Zero

• DOI: 10.1007/s00026-022-00587-2
• Publication Date: 2022-05-25T12:02:31Z
• Authors: Takahide Adachi; Toshitaka Aoki
• Keywords: Zero (linguistics); Cube (algebra); Isomorphism (crystallography); Algebraically closed field

14 pages<br/>In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a complete list of symmetric algebras with radical cube zero having only finitely many isomorphism classes of two-term tilting complexes in terms of their associated graphs. Secondly, we enumerate the number of two-term tilting complexes for each case in the list.<br/>