### Abstract

Let R be a Koszul algebra over a field k and M be a linear R-module. We study a graded subalgebra Δ_{M} of the Ext-algebra Ext_{R}^{⁎}(M,M) called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of R and to periodicity of linear modules are given. Viewing R as a linear module over its enveloping algebra, we also show that Δ_{R} is isomorphic to the graded center of the Koszul dual of R. When R is selfinjective and not necessarily graded, we study connections between periodic modules M, complexity of M and existence of non-nilpotent elements of positive degree in the Ext-algebra of M. Characterizations of periodic algebras are given.

Original language | English (US) |
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Pages (from-to) | 847-866 |

Number of pages | 20 |

Journal | Journal of Pure and Applied Algebra |

Volume | 221 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2017 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Journal of Pure and Applied Algebra*,

*221*(4), 847-866. https://doi.org/10.1016/j.jpaa.2016.08.007