Cohomology Algebras of a Family of DG Skew Polynomial Algebras
Abstract
:1. Introduction
2. Preliminaries
2.1. Notations and Conventions
- 1 .
- If (resp. , then is called the left (resp. right) Gorenstein (cf. [37]);
- 2 .
- If , or equivalently , has a minimal semi-free resolution with a semi-basis concentrated in degree 0, then is called Koszul (cf. [38]);
- 3 .
- If , or equivalently the DG -module is compact, then is called homologically smooth (cf. [39] (Corollary 2.7));
- 4 .
2.2. AS-Gorenstein (AS-Regular) Graded Algebras
3. Some Basic Lemmas
4. Computations of
5. Some Applications
- 1.
- and ;
- 2.
- , and ;
- 3.
- , and ;
- 4.
- , and ;
- 5.
- and ;
- 6.
- and .
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Mao, X.; Ren, G. Cohomology Algebras of a Family of DG Skew Polynomial Algebras. Mathematics 2023, 11, 1617. https://doi.org/10.3390/math11071617
Mao X, Ren G. Cohomology Algebras of a Family of DG Skew Polynomial Algebras. Mathematics. 2023; 11(7):1617. https://doi.org/10.3390/math11071617
Chicago/Turabian StyleMao, Xuefeng, and Gui Ren. 2023. "Cohomology Algebras of a Family of DG Skew Polynomial Algebras" Mathematics 11, no. 7: 1617. https://doi.org/10.3390/math11071617
APA StyleMao, X., & Ren, G. (2023). Cohomology Algebras of a Family of DG Skew Polynomial Algebras. Mathematics, 11(7), 1617. https://doi.org/10.3390/math11071617