The structure of AS-Gorenstein algebras

By Hiroyuki Minamoto, I. Mori. 2011

92 citations recorded by the source corpus.

Abstract In this paper, we define a notion of AS-Gorenstein algebra for N -graded algebras, and show that symmetric AS-regular algebras of Gorenstein parameter 1 are exactly preprojective algebras of quasi-Fano algebras. This result can be compared with the fact that symmetric graded Frobenius algebras of Gorenstein parameter −1 are exactly trivial extensions of finite-dimensional algebras. The results of this paper suggest that there is a strong interaction between classification problems in noncommutative algebraic geometry and those in representation theory of finite-dimensional algebras.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8372c4054b76dc2752e9bdbd7fc3dbe35ff457eb

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In Algebra and Number Theory

1. D. Rogalski
2. Manuel Reyes
3. James J. Zhang
4. U. Krähmer
5. Amnon Yekutieli
6. Kenneth A. Brown

In Geometry and Topology

1. D. Rogalski
2. Manuel Reyes
3. James J. Zhang
4. Amnon Yekutieli
5. U. Krähmer
6. Kenneth A. Brown
7. Masaki Kashiwara

Citations in the corpus

• Skew Calabi–Yau algebras and homological identities (2013, background): “rphism). Remark 3.4. Other notions of generalized AS regular algebras were introduced for not necessarily connected graded algebras by Martinez-Villa and Solberg in [M-VS] and by Minamoto and Mori in [MM]. Even if Ais noetherian of finite global dimension, our definition above is slightly stronger tha”