Algèbre
The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations
Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 739-749.

Let A be a noncommutative Artin–Schelter regular algebra of dimension 2 with the Nakayama automorphism μ A and U a PBW deformation of A with the Nakayama automorphism μ U . We prove that any graded Ore extension A[z;μ A ,δ] and any filtered Ore extension U[z;μ U ,δ ˜] are 3-Calabi–Yau.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.268
Classification : 16S36, 16S37, 16S38, 16S80, 16E65
Shen, Yuan 1 ; Guo, Yang 1

1 Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
@article{CRMATH_2022__360_G7_739_0,
     author = {Shen, Yuan and Guo, Yang},
     title = {The {Calabi{\textendash}Yau} property of {Ore} extensions of two-dimensional {Artin{\textendash}Schelter} regular algebras and their {PBW} deformations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {739--749},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G7},
     year = {2022},
     doi = {10.5802/crmath.268},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.268/}
}
TY  - JOUR
AU  - Shen, Yuan
AU  - Guo, Yang
TI  - The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 739
EP  - 749
VL  - 360
IS  - G7
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.268/
DO  - 10.5802/crmath.268
LA  - en
ID  - CRMATH_2022__360_G7_739_0
ER  - 
%0 Journal Article
%A Shen, Yuan
%A Guo, Yang
%T The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations
%J Comptes Rendus. Mathématique
%D 2022
%P 739-749
%V 360
%N G7
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.268/
%R 10.5802/crmath.268
%G en
%F CRMATH_2022__360_G7_739_0
Shen, Yuan; Guo, Yang. The Calabi–Yau property of Ore extensions of two-dimensional Artin–Schelter regular algebras and their PBW deformations. Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 739-749. doi : 10.5802/crmath.268. http://www.numdam.org/articles/10.5802/crmath.268/

[1] Berger, Roland; Pichereau, Anne Calabi–Yau algebras viewed as deformations of Poisson algebras, Algebr. Represent. Theory, Volume 17 (2014) no. 3, pp. 735-773 | DOI | MR | Zbl

[2] Berger, Roland; Taillefer, Rachel Poincaré–Birkhoff–Witt deformations of Calabi–Yau algebras, J. Noncommut. Geom., Volume 1 (2007) no. 2, pp. 241-270 | DOI | Zbl

[3] Bocklandt, Raf Graded Calabi–Yau algebras of dimension 3, J. Pure Appl. Algebra, Volume 212 (2008) no. 1, pp. 14-32 | DOI | MR | Zbl

[4] Braverman, Alexander; Gaitsgory, Dennis Poincaré–Birkhoff–Witt theorem for quadratic algebras of Koszul type, J. Algebra, Volume 181 (1996) no. 2, pp. 315-328 | DOI | Zbl

[5] Dubois-Violette, Michel Multilinear forms and graded algebras, J. Algebra, Volume 317 (2007) no. 1, pp. 198-225 | DOI | MR | Zbl

[6] Ginzburg, Victor Calabi–Yau algebras (2007) (https://arxiv.org/abs/math/0612139)

[7] Goodman, Jake; Krähmer, Ulrich Untwisting a twisted Calabi–Yau algebra, J. Algebra, Volume 406 (2014), pp. 272-289 | DOI | MR | Zbl

[8] He, Ji-Wei; Van Oystaeyen, Fred; Zhang, Yinhuo Deformations of Koszul Artin–Schelter Gorenstein algebras, Manuscr. Math., Volume 141 (2013) no. 3-4, pp. 463-483 | MR | Zbl

[9] He, Ji-Wei; Van Oystaeyen, Fred; Zhang, Yinhuo Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras, J. Algebra, Volume 390 (2013), pp. 231-249 | MR | Zbl

[10] He, Ji-Wei; Van Oystaeyen, Fred; Zhang, Yinhuo Graded 3-Calabi–Yau algebras as Ore extensions of 2-Calabi–Yau algebras, Proc. Am. Math. Soc., Volume 143 (2015) no. 4, pp. 1423-1434 | MR | Zbl

[11] Liu, Liyu; Ma, Wen Nakayama automorphisms of Ore extensions over polynomial algebras, Glasg. Math. J., Volume 62 (2020) no. 3, pp. 518-530 | DOI | MR | Zbl

[12] Liu, Liyu; Wang, Shengqiang; Wu, Quanshui Twisted Calabi–Yau property of Ore extensions, J. Noncommut. Geom., Volume 8 (2014) no. 2, pp. 587-609 | DOI | MR | Zbl

[13] Minamoto, Hiroyuki; Mori, Izuru The structure of AS-Gorenstein algebras, Adv. Math., Volume 226 (2011) no. 5, pp. 4061-4095 | DOI | MR | Zbl

[14] Mori, Izuru; Smith, S. Paul m-Koszul Artin-Schelter regular algebras, J. Algebra, Volume 446 (2016), pp. 373-399 corrigendum in ibid. 493 (2018), p. 500-501 | DOI | MR | Zbl

[15] Piontkovski, Dmitri Coherent algebras and noncommutative projective lines, J. Algebra, Volume 319 (2008) no. 8, pp. 3280-3290 | DOI | MR | Zbl

[16] Polishchuk, Alexander Noncommutative proj and coherent algebras, Math. Res. Lett., Volume 12 (2005) no. 1, pp. 63-74 | DOI | MR | Zbl

[17] Reyes, Manuel; Rogalski, Daniel; Zhang, James J. Skew Calabi–Yau algebras and homological identities, Adv. Math., Volume 264 (2014), pp. 308-354 | DOI | MR | Zbl

[18] Shen, Yuan; Guo, Yang Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras, J. Algebra, Volume 579 (2021), pp. 114-151 | DOI | MR | Zbl

[19] Shen, Yuan; Lu, Diming Nakayama automorphisms of PBW deformations and Hopf actions, Sci. China, Math., Volume 59 (2016) no. 4, pp. 661-672 | DOI | MR | Zbl

[20] Smith, S. Paul A 3-Calabi–Yau algebra with G 2 symmetry constructed from the Octonions (2011) (https://arxiv.org/abs/1104.3824)

[21] Wu, Quanshui; Zhu, Ruipeng Nakayama automorphisms and modular derivations in filtered deformations, J. Algebra, Volume 572 (2021), pp. 381-421 | MR | Zbl

[22] Zhang, James J. Non-Noetherian regular rings of dimension 2, Proc. Am. Math. Soc., Volume 126 (1998) no. 6, pp. 1645-1653 | DOI | MR | Zbl

Cité par Sources :