Álgebras de Hopf y extensiones PBW torcidas
DOI:
https://doi.org/10.19053/01217488.v10.n2.2019.8797Palabras clave:
Álgebras de Hopf, extensiones PBW torcidas, extensiones de Ore, extensiones de Ore generalizadasResumen
En este artículo se relacionan algunas estructuras de álgebra de Hopf sobre extensiones de Ore y extensiones PBW torcidas de un álgebra de Hopf. Estas relaciones son ilustradas con ejemplos. También se demuestr que las extensiones Hopf Ore y las extensiones Hopf Ore generalizadas son extensiones PBW torcidas de Hopf.
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Referencias
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[2] K.A. Brown, S. O’Hagan, J.J. Zhang, G.Zhuang, “Connected Hopf algebras and iterated Ore extensions”, J. Pure Appl. Algebra,vol. 219, no. 6, pp. 2405-2433, 2015.
[3] C. Gallego, O. Lezama, “Gröbner bases forideals of σ -PBW extensions”, Comm. Algebra,vol. 39, pp. 50-75, 2011.
[4] P. Gilmartin, “Connected Hopf algebras of finite Gelfand-Kirillov dimension”, PhD thesis,University of Glasgow, 2016.
[5] J. Gómez, H. Suárez, “Algunas propiedades homológicas del plano de Jordan”, Ciencia en Desarrollo, vol. 9, no. 2, pp. 69-82, 2018.
[6] N.R. González, Y.P. Suárez, “Ideales en el Anillo de Polinomios Torcidos R[x; σ, δ ]”, Ciencia en Desarrollo, vol. 5, no. 1, pp. 31-37, 2014.
[7] M. Hazewinkel, N. Gubareni and V. Kirichenko, “Algebras, Rings and Modules: Lie Algebras and Hopf Algebras”, Mathematical survey and monographas 168, AMS (2010).
[8] G. Karaali, “On Hopf algebras and their generalizations”, Comm. Algebra, vol. 36, no. 12, pp. 4341-4367, 2008.
[9] O. Lezama, E. Latorre, “Non-commutative algebraic geometry of semi-graded rings”, Internat. J. Algebra Comput., vol. 27, no. 4, pp. 361-389, 2017.
[10] A.N. Panov, “Ore extensions of Hopf algebras”, Math. Notes, vol. 74, no. 3, pp. 401-410, 2003.
[11] R. Ray, “Introduction to Hopf algebras”. Washington: University Gonzaga, 2004. Disponible en: http://web02.gonzaga.edu/faculty/rayr/SpokaneColloquium.pdf (20/12/2018, last visit).
[12] A. Reyes, H. Suárez, “A notion of compatibility for Armendariz and Baer properties over skew PBW extensions”, Rev. Un. Mat. Argentina, vol. 59, no. 1, pp. 157-178, 2018.
[13] A. Reyes, H. Suárez, “PBW bases for some 3-dimensional skew polynomial algebras”, Far East J. Math. Sci. (FJMS), vol. 101, no. 6, pp. 1207-1228, 2017.
[14] A. Reyes, H. Suárez, “PBW extensions of skew Armendariz rings”, Adv. Appl. Clifford Algebr., vol. 27, pp. 3197-3224, 2017.
[15] A. Reyes and H. Suárez, “Enveloping algebra and skew Calabi-Yau algebras over skew Poincaré-Birkhoff-Witt extensions”, Far East J. Math. Sci. (FJMS), vol. 102, no. 2, pp. 373-397, 2017.
[16] A. Reyes and H. Suárez, “Bases for quantum algebras and skew Poincaré-Birkhoff-Witt extensions”, Momento, vol. 54, no. 1, pp. 54-75, 2017.
[17] A. Reyes and H. Suárez, “PBW bases for some 3-dimensional skew polynomial algebras”, Far East J. Math. Sci. (FJMS), vol. 101, no. 6, pp. 1207-1228, 2017.
[18] A. Reyes, H. Suárez, “Some remarks about the cyclic homology of skew PBW extensions”, Ciencia en Desarrollo, vol. 7, no. 2, pp. 99-107, 2016.
[19] M. Ribeiro, “Hopf Algebras and Ore Extensions”, Dissertação Mestrado em Matemática, Universidade do Porto, 2016.
[20] H. Suárez, “Koszulity for graded skew PBW extensions”, Comm. Algebra, vol. 45, no. 10, pp. 4569-4580, 2017.
[21] H. Suárez, O. Lezama, A. Reyes, “Some Relations between N-Koszul, Artin-Schelter Regular and Calabi-Yau with Skew PBW Extensions”, Ciencia en Desarrollo, vol. 6, no. 2, pp. 205-213, 2015.
[22] H. Suárez, O. Lezama, A. Reyes, “Calabi-Yau property for graded skew PBW extensions”, Rev. Colombiana Mat., vol. 51, no. 2, pp. 221- 238, 2017.
[23] H. Suárez, A. Reyes, “Koszulity for skew PBW extension over fields”, JP J. Algebra Number Theory Appl., vol. 39, no. 2, pp. 181-203, 2017.
[24] L. You, Z. Wang, H.X. Chen, “Generalized Hopf Ore extensions”, J. Algebra, vol. 508, pp. 390-417, 2018.
[25] D.-G. Wang, J.J. Zhang and G. Zhuang, “Connected Hopf algebras of Gelfand-Kirillov dimension four”, Trans. Amer. Math. Soc., vol.376, no. 8, pp. 5597-5632, 2015.
[26] G. Zhuang, “Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension”, J. London Math. Soc., vol. 87, no. 2, 877-898, 2013..
