Some homological properties of Jordan plane
![](https://revistas.uptc.edu.co/public/journals/20/cover_issue_550_es_ES.jpg)
Abstract
The Jordan plane can be seen as a quotient algebra, as a graded Ore extension and as a graded skew PBW extension. Using these interpretations, it is proved that the Jordan plane is an Artin-Schelter regular algebra and a skew Calabi-Yau algebra, in addition its Nakayama automorphism is explicitly calculated.Keywords
Jordan plane, Artin-Schelter regular algebras, skew Calabi-Yau algebras, Nakayama automorphism
Author Biography
Hector Julio Suárez Suárez
Boyacá, Tunja
References
- M. Artin y W. Schelter, “Graded Algebras of Global Dimension 3”, Advances in Mathematics, vol. 66, pp. 171-206, 1987. DOI: https://doi.org/10.1016/0001-8708(87)90034-X
- C. Gallego y O. Lezama, “Gröbner bases for ideals of s
- V. Ginzburg, “Calabi-Yau algebras”, arXiv:math.AG/0612139v3, vol. 51, pp. 329-333, 2006.
- N. R. González y Y. P. Suárez, “Ideales en el Anillo de Polinomios Torcidos R[x;s;d]", Ciencia en Desarrollo, vol. 5, no. 1, pp. 31-37, 2014. DOI: https://doi.org/10.19053/01217488.3229
- J. Goodman y U. Krähmer, “Untwisting a twisted Calabi-Yau algebra”, Journal of Algebra, vol. 406, pp. 272-289, 2014. DOI: https://doi.org/10.1016/j.jalgebra.2014.02.018
- J.W He, F. Oystaeyen y Y. Zhang, “Calabi-Yau algebras and their deformations”, Bull. Math. Soc. Sci. Math. Roumanie, vol. 56, no. 3, pp. 335-347, 2013.
- S. Korenskii, “Representations of the Quantum group SLj(2)”, Rus.Math.Surv, vol. 46, no. 6, pp. 211-212, 1991. DOI: https://doi.org/10.1070/RM1991v046n06ABEH002864
- G. R. Krause y T. H. Lenagan, “Growth of algebras and Gelfand-Kirillov dimension”, American Mathematical Soc., 2000. DOI: https://doi.org/10.1090/gsm/022
- O. Lezama and E. Latorre, “Non-commutative algebraic geometry of semi-graded rings”, International Journal of Algebra and Computation, vol. 27, no. 4, pp. 361-389, 2017. DOI: https://doi.org/10.1142/S0218196717500199
- L. Liu, S.Wang y Q.Wu, “Twisted Calabi-Yau property of Ore extensions”, J. Noncommut. Geom., vol. 8, no. 2, pp. 587-609, 2014. DOI: https://doi.org/10.4171/JNCG/165
- A. Reyes and H. Suárez, “Some remarks about the cyclic homology of skew PBW extensions", Ciencia en Desarrollo, vol. 7, no. 2, pp. 99-107, 2016. DOI: https://doi.org/10.19053/01217488.v7.n2.2016.4219
- M. Reyes, D. Rogalski y J. J Zhang “Skew Calabi-Yau algebras and homological identities”, Advances in Mathematics, vol. 264, pp. DOI: https://doi.org/10.1016/j.aim.2014.07.010
- -354, 2014.
- D. Rogalski“ An introduction to noncommutative projective algebraic geometry”, arXiv:1403.3065 [math.RA], 2014.
- H. Suárez, “Koszulity for graded skew PBW extensions”, Communications in Algebra, vol. 45, no. 10, pp. 4569-4580, 2017. DOI: https://doi.org/10.1080/00927872.2016.1272694
- H. Suárez, O. Lezama y A. Reyes, “Some Relations between N-Koszul, Artin-Schelter Regular and Calabi-Yau with Skew PBW Extensions”, Revista Ciencia en Desarrollo, vol. 6, no. 2, pp. 205-213, 2015. DOI: https://doi.org/10.19053/01217488.3791
- H. Suárez, O. Lezama y A. Reyes, “Calabi-Yau property for graded skew PBW extensions”, Revista Colombiana de Matemáticas, vol. 51, no. 2, pp. 221-238, 2017. DOI: https://doi.org/10.15446/recolma.v51n2.70902
- H. Suárez y A. Reyes, “Koszulity for skew PBW extension over fields”, JP Journal of Algebra, Number Theory and Applications, vol.
- , no. 2, pp. 181-203, 2017.
Downloads
Download data is not yet available.