Artículos/Articles

Preprints in arxiv: Please click here.

  1. Root systems in Lie Theory: From the classic definition to nowadays. Notices of the AMS, to appear.
  2. Semisimplification of contragredient Lie algebras (with J. Plavnik and G. Sanmarco)
  3. Finite GK-dimensional Nichols algebras of diagonal type and finite root systems (with A. García Iglesias).
  4. Pointed Hopf algebras over non-abelian groups with non-simple standard braidings (with S. Lentner and G. Sanmarco). Proc. London Math. Soc., to appear.
  5. Corrigendum: Liftings of Jordan planes (with N. Andruskiewitsch and I. Heckenberger). Proc. Edinb. Math. Soc., to appear.
  6. Finite GK-dimensional pre-Nichols algebras of (super)modular and unidentified type (with E. Campagnolo and G. Sanmarco). J. Noncomm. Geom., to appear.
  7. Rank 4 Nichols algebras of pale braidings (with N. Andruskiewitsch and M. Moya Giusti). SIGMA, to appear.
  8.  On finite GK-dimensional Nichols algebras of diagonal type: rank 3 and Cartan type  (with A. García Iglesias). See the log and GAP files. Publicacions Matemàtiques, to appear.
  9. Finite GK-Dimensional pre-Nichols algebras of super and standard type (with E. Campagnolo and G. Sanmarco). J. Pure App. Algebra, to appear.
  10. Poisson orders on large quantum groups (with N. Andruskiewitsch and M. Yakimov). Adv. Math., to appear.
  11. On the Hopf Algebra Structure of the Lusztig Quantum Divided Power Algebras (with N. Andruskiewitsch and C. Vay). Ann. Math. Blaise Pascal 27, No. 2, 131-157 (2020).
  12. Cohomology rings of finite-dimensional pointed Hopf algebras over abelian groups, I & II (with N. Andruskiewitsch, J. Pevtsova, S. Witherspoon). Res. Math. Sci. 9:12 (2022) https://doi.org/10.1007/s40687-021-00287-y
  13. Lie algebras arising from Nichols algebras of diagonal type (with N. Andruskiewitsch and F. Rossi Bertone). IMRN, to appear. https://doi.org/10.1093/imrn/rnab348
  14. Pointed Hopf algebras over non abelian groups with decomposable braidings, I (with G. Sanmarco). See the log and GAP files. J. Algebra 549 (2020), 78-111.
  15. Examples of finite-dimensional pointed Hopf algebras in positive characteristic (with N. Andruskiewitsch and I. Heckenberger). In Representation Theory, Mathematical Physics and Integrable Systems, in honor of Nicolai Reshetikhin, editors A. Alexeev, E. Frenkel, M. Rosso, B. Webster and M. Yakimov. Progr. Math. 340, pp 1-38 (2021). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-78148-4_1
  16. Pointed Hopf algebras: a guided tour to the liftings (with A. García Iglesias). Revista Colombiana de Matemáticas: Proceedings of "XXII CLA Coloquio Latinoamericano de Algebra" 53 (2019), 1-44. See the log and GAP files. 
  17. On Nichols algebras of infinite rank with finite Gelfand-Kirillov dimension (with N. Andruskiewitsch and I. Heckenberger). Rend. Lincei Mat. Appl. 31 (2020), 81–101.  DOI 10.4171/RLM/880.
  18. On finite GK-dimensional Nichols algebras of diagonal type (with N. Andruskiewitsch and I. Heckenberger). Contemp. Math. 728 (2019), 1-23.
  19. On Nichols algebras over basic Hopf algebras (with N. Andruskiewitsch). Math. Z. 296 (2020), 1429-1469.
  20. Pointed finite tensor categories over abelian groups (with C. Galindo). Int. J. Math.  28, No. 11, 1750087 (2017)
  21. On finite dimensional Nichols algebras of diagonal type (with N. Andruskiewitsch). Bulletin of Mathematical Sciences, December 2017, Volume 7, Issue 3, 353–573.
  22. Bruhat order and nil-Hecke algebras for Weyl groupoids (with H. Yamane) . J. Algebra Appl.  17, No. 09, 1850166 (2018).
  23. Simple Modules of the Quantum Double of the Nichols Algebra of Unidentified Diagonal Type ufo(7) (with N. Andruskiewitsch, A. Mejía and C. Renz). Comm. Alg. 46 (2018), 1170-1798.
  24. A quantum version of the algebra of distributions of SL2. Proc. RIMS 54 (2018), 141-161.
  25. On finite GK-dimensional Nichols algebras over abelian groups (with N. Andruskiewitsch and I. Heckenberger). Mem. Amer. Math. Soc. 271, Number 1329 (2021). 
  26. Liftings of Nichols algebras of diagonal type II. All liftings are cocycle deformations (with A. García Iglesias). Selecta Math. (2019). doi: 10.1007/s00029-019-0452-4. See the log and GAP files.
  27. Hopf braces and Yang-Baxter operators (with C. Galindo and L. Vendramin). Proc. Amer. Math. Soc. 145 (2017), 1981-1995.
  28. A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2) (with N. Andruskiewitsch and F. Rossi Bertone). Bull. Belg. Math. Soc. Simon Stevin 24 (2017) 15–34.
  29. Liftings of Jordan and super Jordan planes (with N. Andruskiewitsch and I. Heckenberger). Proc. Edinb. Math. Soc., II. Ser. 61 (2018), no. 3, 661-672.
  30. Cohomology and Coquasi-bialgebras in the category of Yetter-Drinfeld Modules (with A. Ardizzoni and C. Menini). Ann. Scuola Norm. Sup. Pisa Cl. Sci.(5) Vol. XVII (2017), 609-653.
  31. Liftings of Nichols algebras of diagonal type I. Cartan type A (with N. Andruskiewitsch and A. García Iglesias). IMRN 9 (2017), 2793–2884.
  32. The quantum divided power algebra of a finite-dimensional Nichols algebra of diagonal type (with N. Andruskiewitsch and F. Rossi Bertone). Math. Research Letters 24 (2017), 619-643.
  33. On rigidity of Nichols algebras (with M. Kochetov and M. Mastnak). J. Pure Appl. Alg. 219 (2015), 5539-5559.
  34. Distinguished Pre-Nichols algebras. Transf. Groups 21 (2016), 1-33.
  35. The R-matrix of quantum doubles of Nichols algebras of diagonal type (with H. Yamane). J. Math. Phys. 56, No. 2, 021702, 19 p. (2015).
  36. Liftings via cocycle deformations (with N. Andruskiewitsch, A. García Iglesias, A. Masuoka and C. Vay). J. Pure Appl. Alg. 218 (2014), 684-703.
  37. Examples of pointed color Hopf algebras (with N. Andruskiewitsch and D. Bagio). J. Algebra Appl. 13, 1350098 (2014) [28 pages] DOI: 10.1142/S0219498813500989
  38. De-equivariantization of Hopf algebras (with C. Galindo and M. Pereira). Alg. Rep. Theory 17 (2014), 161-180.
  39. From Hopf algebras to tensor categories (with N. Andruskiewitsch, A. García Iglesias, B. Torrecillas and C. Vay). Conformal field theories and tensor categories, pages 1-32. Proceedings of a Workshop Held at Beijing International Center for Math. Research Series: Mathematical Lectures from Peking Univ. Bai, C., Fuchs, J., Huang, Y.-Z., Kong, L., Runkel, I., Schweigert, C. (Eds.) 2014, IX, 279 p. Springer. ISBN 978-3-642-39383-9
  40. Nichols algebras of unidentified diagonal type. Comm. Alg 41 (2013), 4667-4693.
  41. On Nichols algebras of diagonal type. J. Reine Angew. Math. 683 (2013), 189-251.
  42. On pointed Hopf superalgebras (with N. Andruskiewitsch and H. Yamane). Contemp. Math. 544 (2011), 123-140.
  43. A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems. J. Europ. Math. Soc. 17 (2015), 2643-2671.
  44. Pointed hopf algebras with standard braiding are generated in degree one (with A. García Iglesias). Contemp. Math. 537 (2011), 57-70.
  45. Basic quasi-Hopf algebras over cyclic groups. Adv. Math. 225 (2010), 3545-3575.
  46. On Nichols algebras with standard braiding. Algebra & Number Theory, Vol. 3 (2009), 35-106.
  47. On Nichols algebras with generic braiding (with N. Andruskiewitsch). In "Modules and Comodules". Trends in Mathematics. Brzezinski, T.; Gómez Pardo, J.L.; Shestakov, I.; Smith, P.F. (Eds.), pp. 47-64 (2008).

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