El automorfismo de Nakayama de algunas extensiones PBW torcidas

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Héctor Suárez https://orcid.org/0000-0003-4618-0599
Armando Reyes https://orcid.org/0000-0002-5774-0822

Keywords

Extensiones PBW torcidas, automorfismo de Nakayama, álgebras Artin-Schelter regulares, álgebras Calabi-Yau

Resumen

Sean R un álgebra Artin-Schelter regular y A = σ(R)⟨x1,...,xn   una extensión PBW torcida cuasi-conmutativa graduada sobre R. En este artículo se describe el automorfismo de Nakayama de A usando el automorfismo de
Nakayama del anillo de coeficientes R. También se calcula explícitamente el automorfismo de Nakayama de algunas extensiones PBW torcidas. 

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Referencias

[1] M. Reyes, D. Rogalski, and J. J. Zhang, “Skew Calabi-Yau algebras and homological identities,” Adv. in Math., vol. 264, pp. 308–354, 2014.

[2] L.-Y. Liu, S. Wang, and Q.-S. Wu, “Twisted Calabi-Yau property of Ore extensions,” J. Noncommut. Geom., vol. 8, no. 2, pp. 587–609, 2014.

[3] J.-F. Lü, X.-F. Mao, and J. Zhang, “Nakayama automorphism and applications,” Tran. Amer. Math. Soc., vol. 369, pp. 2425–2460, 2017. [Online]. Available: https://doi.org/10.1090/tran/6718

[4] J.-F. Lü, X.-F. Mao, and J. J. Zhang, “The nakayama automorphism of a class of graded algebras,” Israel Journal of Mathematics, vol. 219, no. 2, pp. 707–725, Apr 2017. [Online]. Available: https: //doi.org/10.1007/s11856-017-1495-x

[5] Y. Shen, G.-S. Zhou, and D.-M. Lu, “Nakayama automorphisms of twisted tensor products,” Journal of Algebra, vol. 504, no. 15, pp. 445 – 478, 2018. [Online]. Available: https://doi.org/10.1016/j.jalgebra.2018.02.025

[6] Y. Liu and W. Ma, “Nakayama automorphism of Ore extensions over polynomial algebras,” arXiv:1808.03589v1 [math.RA], pp. 1–12, 2018.

[7] C. Gallego and O. Lezama, “Gröbner bases for ideals of σ-PBW extensions,” Comm. Algebra, vol. 39, no. 1, pp. 50–75, 2011.

[8] O. Lezama and A. Reyes, “Some homological properties of skew PBW extensions,” Comm. Algebra, vol. 42, pp. 1200–1230, 2014.

[9] H. Suárez, “Koszulity for graded skew PBW extensions,” Communications in Algebra, vol. 45, no. 10, pp. 4569–4580, 2017. [Online]. Available: https://doi.org/10.1080/00927872.2016.1272694

[10] H. Suárez, “N-Koszul algebras, Calabi-Yau algebras and skew PBW extensions,” Ph.D. Thesis, Universidad Nacional de Colombia, sede Bogotá, 2017.

[11] A. Reyes and J. Jaramillo, “Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions,” Ingenieria y Ciencia, vol. 14, no. 27, pp. 29–52, 2018. [Online]. Available: https://doi.org/10.17230/ingciencia.14.27.2

[12] A. Reyes and H. Suárez, “Enveloping algebra and Calabi-Yau algebras over skew Poincaré-Birkhoff-Witt extensions,” Far East J. Math. Sci. (FJMS), vol. 102, no. 2, pp. 373–397, 2017.

[13] A. Reyes and H. Suárez, “A notion of compatibility for Armendariz and baer properties over skew PBW extensions,” Revista de la Unión Matemática Argentina, vol. 59, no. 1, pp. 157–178, 10 2017. [Online]. Available: https://doi.org/10.33044/revuma.v59n1a08

[14] ——, “σ-PBW extensions of skew Armendariz rings,” Advances in Applied Clifford Algebras, vol. 27, pp. 3197–3224, 11 2016. [Online]. Available: https://doi.org/10.1007/s00006-017-0800-4

[15] H. Suárez and A. Reyes, “Koszulity for skew pbw extensions over fields,” JP Journal of Algebra, Number Theory and Applications, 39 (2), 2017, 181-203. [Online]. Available: https://doi.org/10.17654/NT039020181

[16] 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.

[17] H. Suárez, O. Lezama, and A. Reyes, “Calabi-Yau property for graded skew PBW extensions,” Rev. Colombiana Mat., vol. 51, no. 2, pp. 221–238, 2017.

[18] D. Rogalski, Noncommutative projective geometry. In Noncommutative algebraic geometry. vol. 64 of Math. Sci. Res. Inst. Publ., 13-70, 64th ed. New York: Cambridge Univ. Press, 2016.

[19] J. Goodman and U. Krähmer, “Untwisting a twisted Calabi-Yau algebra,” J. Algebra, vol. 406, pp. 271–289, 2014.

[20] R. Berger and R. Taillefer, “Poincaré-Birkhoff-Witt deformations of CalabiYau algebras,” J. Noncommut. Geom., vol. 1, pp. 241–270, 2007.

[21] K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, 2nd ed. London: London Mathematical Society Student Texts, 2004.

[22] J. Gómez and H. Suárez, “Algunas propiedades homológicas del plano de Jordan,” Ciencia en Desarrollo, vol. 9, no. 2, pp. 67–80, 2018.

[23] R. Berger, “Gerasimov’s theorem and N-Koszul algebras,” J. London Math. Soc., vol. 79, pp. 631–648, 2009.

[24] C. Zhu, F. V. Oystaeyen, and Y. Zhang, “Nakayama automorphism of double Ore extensions of Koszul regular algebras,” Manuscripta math., vol. 152, no. 3-4, pp. 555–584, 2017.