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DG polynomial algebras and their homological properties
- Source :
- Science China Mathematics. 62:629-648
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- In this paper, we introduce and study differential graded (DG for short) polynomial algebras. In brief, a DG polynomial algebra $\mathcal{A}$ is a connected cochain DG algebra such that its underlying graded algebra $\mathcal{A}^{\#}$ is a polynomial algebra $\mathbb{k}[x_1,x_2,\cdots, x_n]$ with $|x_i|=1$, for any $i\in \{1,2,\cdots, n\}$. We describe all possible differential structures on DG polynomial algebras; compute their DG automorphism groups; study their isomorphism problems; and show that they are all homologically smooth and Gorestein DG algebras. Furthermore, it is proved that the DG polynomial algebra $\mathcal{A}$ is a Calabi-Yau DG algebra when its differential $\partial_{\mathcal{A}}\neq 0$ and the trivial DG polynomial algebra $(\mathcal{A}, 0)$ is Calabi-Yau if and only if $n$ is an odd integer.<br />It has been accepted for publication in SCIENCE CHINA Mathematics. 20 pages
- Subjects :
- Polynomial (hyperelastic model)
Mathematics::Commutative Algebra
General Mathematics
010102 general mathematics
Graded ring
Mathematics - Rings and Algebras
010103 numerical & computational mathematics
Automorphism
01 natural sciences
16E45, 16E65, 16W20, 16W50
Combinatorics
Integer
Rings and Algebras (math.RA)
FOS: Mathematics
Calabi–Yau manifold
Isomorphism
0101 mathematics
Algebra over a field
Differential (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi.dedup.....f3a0382c410f1dc7e9dc712f9c2b7d52