Publisher：Annales Scientifiques De L Ecole Normale Superieure  

We study periodicity and twisted periodicity of the trivial extension algebra T (A) of a finite-dimensional algebra A. We show that (twisted) periodicity of T (A) is equivalent to A being (twisted) fractionally Calabi-Yau of finite global dimension. We also extend this result to a large class of self-injective orbit algebras. As a consequence, the results give a partial answer to the periodicity conjecture of Erdmann-Skowroński, which expects the classes of periodic and twisted periodic algebras to coincide. On the practical side, it allows us to construct a large number of new examples of periodic algebras and fractionally Calabi-Yau algebras. We also establish a connection between periodicity and cluster tilting theory, by showing that twisted periodicity of T (A) is equivalent to the d -representation-finiteness of the r -fold trivial extension algebra T<inf>r</inf> (A) for some r, d ≥ 1. This answers a question by Darpö and Iyama. As applications of our results, we give answers to some other open questions. We construct periodic symmetric algebras of wild representation type with arbitrary large minimal period, answering a question by Skowroński. We also show that the class of twisted fractionally Calabi-Yau algebras is closed under derived equivalence, answering a question by Herschend and Iyama.

DOI： 10.24033/asens.2610

Web of Science

Scopus

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.jalgebra.2022.04.002

Web of Science

Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press ({CUP})  

DOI： 10.1017/nmj.2020.1

Web of Science

Scopus

Publishing type：Research paper (scientific journal)  

Publisher：Algebraic Combinatorics  

In the 40s, Mayer introduced a construction of (simplicial) p-complex by using the unsigned boundary map and taking coefficients of chains modulo p.We look at such a p-complex associated to an (n - 1)-simplex; in which case, this is also a p-complex of representations of the symmetric group of rank n - specifically, of permutation modules associated to two-row compositions. In this article, we calculate the so-called slash homology - a homology theory introduced by Khovanov and Qi - of such a p-complex. We show that every non-trivial slash homology group appears as an irreducible representation associated to two-row partitions, and how this calculation leads to a basis of these irreducible representations given by the so-called p-standard tableaux.

DOI： 10.5802/ALCO.153

Open Access

Scopus

Event date： 2016.8 - 2016.9

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2016.3

Language：English   Presentation type：Oral presentation (general)  

Country：Germany  

Event date： 2014.3

Language：English   Presentation type：Oral presentation (general)  

Country：United Kingdom