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Algunos tipos especiales de determinantes en extensiones P BW torcidas graduadas.

  • Autores: Héctor Suárez, Duban Cáceres, Armando Reyes
  • Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 39, Nº. 1, 2021, págs. 91-107
  • Idioma: español
  • DOI: 10.18273/revint.v39n1-2021007
  • Enlaces
  • Resumen
    • español

      En este artículo, demostramos que el automorfismo de Nakayama de una extensión PBW torcida graduada sobre un álgebra de Koszul finitamente presentada y Auslander-regular tiene determinante homológico trivial. Una extensión PBW torcida graduada sobre un álgebra conexa R, calculamos su P-determinante y el inverso de σ. En el caso particular de extensiones PBW torcidas cuasi-conmutativas sobre álgebras de Koszul Artin-Schelter regulares, mostramos explícitamente la relación entre el automorfismo de Nakayama del anillo de coeficientes y la extensión. Finalmente, damos condiciones para garantizar que A sea Calabi-Yau. Proporcionamos ejemplos ilustrativos de la teoría con álgebras de interés en geometría algebraica no conmutativa y geometría diferencial no conmutativa.

    • English

      In this paper, we prove that the Nakayama automorphism ofa graded skew PBW extension over a finitely presented Koszul Auslander-regular algebra has trivial homological determinant. Agraded skew PBW extension over a connected algebraR, we compute itsP-determinant and the inverse ofσ. In the particular case of quasi-commutativeskew PBW extensions over Koszul Artin-Schelter regular algebras, we showexplicitly the connection between the Nakayama automorphism of the ring ofcoefficients and the extension. Finally, we give conditions to guarantee thatAis Calabi-Yau. We provide illustrative examples of the theory concerningalgebras of interest in noncommutative algebraic geometry and noncommu-tative differential geometry.

  • Referencias bibliográficas
    • Referencias Acosta J.P. and Lezama O., “Universal property of skew PBW extensions”, Algebra and Discrete Math., 20 (2015), No. 1, 1-12.
    • Artamonov V.A., “Derivations of skew PBW extensions”, Commun. Math. Stat., 3 (2015), No. 4, 449-457. doi: 10.1007/s40304-015-0067-9
    • Artin M. and Schelter W.F., “Graded algebras of global dimension 3”, Adv. Math., 66 (1987), 171-216. doi: 10.1016/0001-8708(87)90034-X
    • Backelin J. and Fröberg R., “Koszul algebras, Veronese subrings and rings with linear resolutions”, Rev. Roumaine Math. Pures Appl., 30 (1985),...
    • Bell A. and Goodearl K., “Uniform rank over differential operator rings and PoincaréBirkhoff-Witt extensions”, Pacific J. Math., 131 (1988),...
    • Carvalho P., Lopes S. and Matczuk J., “Double Ore extensions versus iterated Ore extensions”, Comm. Algebra, 39 (2011), No. 8, 2838-2848....
    • Fajardo W., Gallego C., Lezama O., Reyes A., Suárez H., and Venegas H., Skew PBW Extensions: Ring and Module-theoretic Properties, Matrix...
    • Gallego C. and Lezama O., “Gröbner bases for ideals of σ-PBW extensions”, Comm. Algebra, 39 (2011), No. 1, 50-75. doi: 10.1080/00927870903431209
    • Gómez J.Y. and Suárez H., “Double Ore extensions versus graded skew PBW extensions”, Comm. Algebra, 48 (2020), No. 1, 185-197.
    • Goodearl K.R. and Warfield R.B. Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 2nd ed., vol. 61, Cambridge,...
    • Hashemi E., Khalilnezhad K. and Alhevaz A., “(Σ, ∆)-Compatible skew PBW extension ring”, Kyungpook Math. J., 57 (2017), No. 3, 401-417. doi:...
    • Hashemi E., Khalilnezhad K. and Alhevaz A., “Extensions of rings over 2-primal rings”, Le Matematiche, 54 (2019), No. 1, 141-162. doi: 10.4418/2019.74.1.10
    • Hashemi E., Khalilnezhad K. and Ghadiri Herati M., “Baer and quasi-Baer properties of skew PBW extensions”, J. Algebraic Systems, 7 (2019),...
    • Isaev A.P., Pyatov P.N. and Rittenberg V., “Diffusion algebras”, J. Phys. A., 34 (2001), No. 29, 5815-5834. doi: 10.1088/0305-4470/34/29/306
    • Jordan D., “The graded algebra generated by two Eulerian derivatives”, Algebr. Represent. Theory, 4 (2001), No. 3, 249-275. doi: 10.1023/A:1011481028760...
    • Lezama O., “Computation of point modules of finitely semi-graded rings”, Comm. Algebra, 48 (2020), No. 2, 866-878. doi: 10.1080/00927872.2019.1666404
    • Lezama O. and Gallego C., “d-Hermite rings and skew PBW extensions”, São Paulo J. Math. Sci., 10 (2016), No. 1, 60-72. doi: 10.1007/s40863-015-0010-8
    • Lezama O. and Gómez J., “Koszulity and Point Modules of Finitely Semi-Graded Rings and Algebras”, Symmetry, 11 (2019), No. 7, 1-22. doi: 10.3390/sym11070881
    • Lezama O. and Reyes A., “Some homological properties of skew PBW extensions”, Comm. Algebra, 42 (2014), No. 3, 1200-1230. doi: 10.1080/00927872.2012.735304
    • Lezama O. and Venegas C., “Center of skew PBW extensions”, Internat. J. Algebra Comput., 30 (2020), No. 8, 1625-1650. doi: 10.1142/S0218196720500575
    • Liu Y. and Ma W., “Nakayama automorphism of Ore extensions over polynomial algebras”, Glasg. Math. J., 62 (2020), No. 3, 518-530. doi: 10.1017/s0017089519000259
    • Liu Y., Wang S. and Wu Q.-S., “Twisted Calabi-Yau property of Ore extensions”, J. Noncommut. Geom., 8 (2014), No. 2, 587-609. doi: 10.4171/JNCG/165
    • Lu J., Mao X. and Zhang J.J., “Nakayama automorphism and applications”, Trans. Amer. Math. Soc., 369 (2017), No. 4, 2425-2460. doi: 10.1090/tran/6718
    • Ore O., “Theory of non-commutative polynomials”, Ann. Math, 34 (1933), No. 3, 480-508. doi: 10.2307/1968173
    • Polishchuk A. and Positselski L., Quadratic algebras, American Mathematical Society, vol. 37, Providence, RI, 2005. doi: 10.1090/ulect/037
    • Reyes M., Rogalski D. and Zhang J.J., “Skew Calabi-Yau algebras and homological identities”, Adv. Math., 264 (2014), 308-354. doi: 10.1016/j.aim.2014.07.010
    • Reyes A. and Suárez H., “Armendariz property for skew P BW extensions and their classical ring of quotients”, Rev. Integr. Temas Mat., 34...
    • Reyes A. and Suárez H., “Enveloping Algebra and Skew Calabi-Yau algebras over Skew Poincaré-Birkhoff-Witt extensions”, Far East J. Math. Sci.,...
    • Reyes A. and Suárez H., “Radicals and Köthe’s conjecture for skew PBW extensions”, Commun. Math. Stat., (2019). doi: 10.1007/s40304-019-00189-0
    • Reyes A. and Suárez H., “Skew Poincaré-Birkhoff-Witt extensions over weak compatible rings”, J. Algebra Appl., 19 (2020), No. 12, 21. doi:...
    • Reyes A. and Suárez H., “Skew Poincaré-Birkhoff-Witt extensions over weak zip rings”, Beitr. Algebra Geom., vol. 60 (2019), No. 2, 197-216....
    • Shen Y. and Lu D.-M., “Nakayama automorphisms of P BW deformations and Hopf actions”, Sci. China Math., 59 (2016), No. 4, 661-672. doi: 10.1007/s11425-015-5077-2
    • Shen Y., Zhou G-S. and Lu D-M., “Nakayama automorphisms of twisted tensor products”, J. Algebra, 504 (2018), 445-478. doi: 10.1016/j.jalgebra.2018.02.025
    • Suárez H., “Koszulity for graded skew PBW extensions”, Comm. Algebra, 45 (2017), No. 10, 4569-4580. doi: 10.1080/00927872.2016.1272694
    • Suárez H., Lezama O. and Reyes A., “Calabi-Yau property for graded skew PBW extensions”, Rev. Colombiana Mat., 51 (2017), No. 2, 221-238....
    • Suárez H. and Reyes A., “Koszulity for skew PBW extensions over fields”, JP J. Algebra Number Theory Appl., 39 (2017), No. 2, 181-203. doi:...
    • Suárez H. and Reyes A., “A generalized Koszul property for skew PBW extensions”, Far East J. Math. Sci., 101 (2017), No. 2, 301-320. doi:...
    • Suárez H. and Reyes A., “Nakayama automorphism of some skew PBW extensions”, Ingeniería y Ciencia, 15 (2019), No. 29, 157-177. doi: 10.17230/ingciencia.15.29.6
    • Tumwesigye A.B., Richter J. and Silvestrov S., Centralizers in PBW extensions, Springer, vol. 317, Cham, 2020. doi: 10.1007/978-3-030-41850-2-20
    • Wu Q. and Zhu C., “Skew group algebras of Calabi-Yau algebras”, J. Algebra, 340 (2011), 53-76. doi: 10.1016/j.jalgebra.2011.05.027
    • Zambrano B.A., “Poisson brackets on some skew PBW extensions”, Algebra Discrete Math., 29 (2020), No. 2, 277-302.
    • Zhang J.J. and Zhang J., “Double Ore extensions”, J. Pure Appl. Algebra, 212 (2008), No. 12, 2668-2690. doi: 10.1016/j.jpaa.2008.05.008
    • Zhang J.J. and Zhang J., “Double extension regular algebras of type (14641)”, J. Algebra, 322 (2009), No. 2, 373-409. doi: 10.1016/j.jalgebra.2009.03.041
    • Zhu C., Van Oystaeyen F. and Zhang Y., “Nakayama automorphisms of double Ore extensions of Koszul regular algebras”, Manuscripta Math., 152...
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