Artículos de Nicolás Andruskiewitsch.

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Artículos / Articles de Nicolás Andruskiewitsch

On twisted homogeneous racks of type D. (With F. Fantino, G. García, L. Vendramin). Abstract and file, arXiv:1007:1739v1.

Pointed Hopf algebras over the sporadic groups. (With F. Fantino, M. Graña, L. Vendramin). Abstract and file, arXiv:1001.1108v1. See here for the log files and other links.

On slim double Lie groupoids. (With J. Ochoa and A. Tiraboschi). Abstract and file, arXiv:0808.3147. 15 pages. Enviado.

On Nichols algebras associated to simple racks. (With F. Fantino, G. García, L. Vendramin). Abstract and file, arXiv:1006.5727v1.Aparecerá en Contemp. Math.
The Nichols algebra of a semisimple Yetter-Drinfeld module. (With I. Heckenberger and H.-J. Schneider ). Abstract and file, arXiv:0803.2430. Aparecerá en Amer. J. Math.

Complete reducibility theorems for modules over pointed Hopf algebras. (With D. Radford and H.-J. Schneider ). Abstract and file, arXiv:1001.3977. 44 pages. Aparecerá en Journal of Algebra, Special Issue in honor of Susan Montgomery.

Finite-dimensional pointed Hopf algebras with alternating groups are trivial. (With F. Fantino, M. Graña, L. Vendramin). Abstract and file, arXiv:00812.4628. 26 pp. Aparecerá en Ann. Mat. Pura Appl. (4)

Examples of inner linear Hopf algebras. (With J. Bichon). Abstract and file, arXiv:0911.5585. 9 pages. Revista de la Unión Matemática Argentina vol. 51-1, pp. 7--18 (2010).

The beginnings of the theory of Hopf algebras. (With Walter Ferrer Santos). pdf Acta Applicandae Mathematicae. Acta Appl Math (2009) 108: 3–17. Revisions available here: arXiv:0901.2460.
Ver también el artículo de Pierre Cartier, Groupes algébriques et groupes de Lie formels, Centre Belge Rech. Math., Colloque Theor. Groupes algebr., Bruxelles 1962, (1962), 87-111.

On pointed Hopf algebras associated with the symmetric groups. (With F. Fantino and S. Zhang). Abstract and file, arXiv:0807.2406. Manuscripta Math., Vol. 128, N. 3 (March 2009). Pages 359-371. Versión publicada.

New techniques for pointed Hopf algebras. (With F. Fantino). Abstract and file, arXiv:0803.3486. New developments in Lie theory and geometry, Contemp. Math. 491 (2009) 323-348.
Quantum subgroups of a simple quantum group at roots of 1. (With G. García). Abstract and file, arXiv:0707.0070. Compositio Math. 145 (2009), 476-500.

On Nichols algebras with generic braiding. (With I. Angiono). Abstract and file,arXiv:math/0703924v2 . In "Modules and Comodules". Trends in Mathematics. Brzezinski, T.; Gómez Pardo, J.L.; Shestakov, I.; Smith, P.F. (Eds.), pp. 47-64 (2008). ISBN: 978-3-7643-8741-9.

On pointed Hopf algebras associated with alternating and dihedral groups. (With F. Fantino). Abstract and file, math.QA/0702559. Rev. Unión Mat. Argent.. 48-3, (2007), pag. 57-71 (versión final).

On module categories over finite-dimensional Hopf algebras . (With J. M. Mombelli). Abstract and file, math.QA/0608781. J. Alg. 314, (2007), 383-418.

On pointed Hopf algebras associated to unmixed conjugacy classes in S_n . (With F. Fantino). Abstract and file, math.QA/0608701. J. Math. Phys. 48, 033502 (2007) (26 pages).

Extensions of finite quantum groups by finite groups . (With G. García). Abstract and file, math/0608647. Transformation Groups Vol. 14, N. 1 (March 2009). Pages 1-27. Versión publicada.

A family of Poisson non-compact symmetric spaces . (With A. Tiraboschi) J. Geom. Phys. 60, issue 10 (octubre 2010), 1306--1325.

The structure of double groupoids . (With S. Natale ). Abstract and file, math.CT/0602497. J. Pure Appl. Algebra Volume 213, Issue 6, June 2009, Pages 1031-1045. Versión publicada.Ver comentarios de R. Brown.

Isomorphism classes and automorphisms of finite Hopf algebras of type A_n . (With H.-J. Schneider ). Abstract and file, math.QA/0511283. Actas del XVI Coloquio Latinoamericano de Álgebra (Colonia, Uruguay), 27 pp; Biblioteca de la Revista Matemática Iberoamericana. Versión final.

On pointed Hopf algebras associated to some conjugacy classes in S_n . (With Shouchuan Zhang ). Abstract and file, math.QA/0511020. Proc. Amer. Math. Soc. 135 (2007), 2723-2731.

On observable module categories . (With Walter Ferrer Santos). pdf. in Groups, Rings and Group Rings, Lecture Notes in Pure and Appl. Math. No 248, Chapman & Hall/CRC, Boca Raton, 2006, pp.11-23.

On the classification of finite-dimensional pointed Hopf algebras . (With H.-J. Schneider ). Abstract and file, math.QA/0502157. Ann. Math. Vol. 171 (2010), No. 1, 375–417. Versión final.

Tensor categories attached to double groupoids. (With Sonia Natale). Abstract and file, math.QA/0408045. Adv. Math. 200 (2006) pp. 539-583.

Examples of weak Hopf algebras arising from vacant double groupoids. (With Juan Martín Mombelli). Abstract and file, math.QA/0405374. Nagoya Math. J. 181 (2006), 1--27.

On the quiver-theoretical quantum Yang-Baxter equation. Abstract and file, math.QA/0402269. Selecta Math., New ser. 11 (2005), 203-246. tex, pdf.

Representations of matched pairs of groupoids and applications to weak Hopf algebras. (With Marcelo Aguiar). Abstract and file, math.QA/0402118. Versión final: pdf. Contemp. Math. 376 (2005), 127-173.

Irreducible representations of liftings of quantum planes. (With M. Beattie). pdf. Proceedings of V International Workshop "Lie Theory and Its Applications in Physics", (Varna, June 2003), eds. H.-D. Doebner and V.K. Dobrev, (World Sci, Singapore, 2004, ISBN 981-238-936-9). Corrected version, math/0609515.

Double categories and quantum groupoids. (With S. Natale). Abstract and file, math.QA/0308228. Versión final, Publ. Mat. Urug. 10 11-51 (2005).

Examples of liftings of Nichols algebras over racks. ps. (With M. Graña). En Algebra Montpellier Announcements, 6 pp.

Some remarks on Nichols algebras. Abstract and file. En "Hopf algebras", Bergen, Catoiu and Chin (eds.), 25-45 (2004), M. Dekker.

The coradical of the dual of a lifting of a quantum plane. (With M. Beattie). dvi. En "Hopf algebras", Bergen, Catoiu and Chin (eds.), 47-63 (2004), M. Dekker.

On simple real Lie bialgebras Abstract and file. (With P. Jancsa). IMRN 2004:3 (2004) 139-158.

On the automorphisms of $U_q^+({\mathfrak g})$. Abstract and file. (With F. Dumas). IRMA Lectures in Mathematics and Theoretical Physics Vol. 12. Quantum Groups pp. 107-134. Versión final.

Braided Hopf algebras arising from matched pairs of groups. Abstract and file. (With S. Natale). J. Pure Appl. Alg. 182, 119--149 (2003).

From racks to pointed Hopf algebras. (With M. Graña) Abstract and file. Adv. in Math. 178 (2), 177--243 (2003).

A characterization of quantum groups . (With H.-J. Schneider ). Abstract and file. J. Reine Angew. Math. 577, 81--104 (2004).

Pointed Hopf algebras . (With H.-J. Schneider). In "New directions in Hopf algebras", MSRI series Cambridge Univ. Press; 1--68 (2002). ps.
Co-Frobenius Hopf algebras and the coradical filtration . (With S. Dascalescu). Math. Z. 243 (2003), no. 1, 145--154. dvi.

On finite quantum groups at -1 . (With S. Dascalescu). Algebr. Represent. Theory 8 (2005), no. 1, 11--34. dvi.

New Trends in Hopf Algebra Theory . (Editor, with W. Ferrer Santos and H.-J. Schneider). Contemporary Mathematics, vol. 267. Amer. Math. Soc. (2000).

Triangular Hopf Algebras With The Chevalley Property . (With P. Etingof and S. Gelaki). Michigan Math. J. 49 (2001), 277--298. Abstract. ps. dvi. Versión publicada

About finite dimensional Hopf algebras . Notes of a course given at the CIMPA School "Quantum symmetries in theoretical physics and mathematics", Bariloche 2000. Contemp. Math 294, 1--57 (2002). ps. See Contemp. Math. 294

Harmonic analysis on semisimple Hopf algebras . (With S. Natale). Algebra i Analiz 12, no. 5, (2000), pp. 3--27. Also in St. Petersburg Math. J. 12, no. 5, 713--733 (2001). ps. pdf

Counting arguments for Hopf algebras of low dimension . (With S. Natale). Tsukuba Math. J. 25, No. 1 (2001), pp. 187--201. Version of March 21, 2000. dvi. tex.

Finite quantum groups over abelian groups of prime exponent . (With H.-J. Schneider). Preprint (1999). Ann. Sci. Ec. Norm. Super. 35 (2002), 1--26. ps publ.

Compact matrix quantum groups arising from hermitian Yang-Baxter coalgebras . (With A. Abella). Commun. Alg. 30 (7), 3107--3142 (2002). ps.

Lie quasi-bialgebras with quasi-triangular decomposition . (With A. Tiraboschi). J. of Lie Theory 10 (2000) 383--397. Abstract. dvi. tex.

Lifting of Nichols Algebras of Type A₂ and Pointed Hopf Algebras of order p⁴ . (With H.-J. Schneider). Proceedings of the Colloquium "Hopf algebras and quantum groups", Brussels 1998, ed. S. Caeneppel, Marcel Dekker, (2000), 1-15. tex. dvi. ps.

On the coradical filtration of Hopf algebras whose coradical is a Hopf subalgebra. (With H.-J. Schneider). Bol. Acad. Nacional de Ciencias (Córdoba) 65 (2000), pp. 45--51. tex. dvi.

Finite quantum groups and Cartan matrices. (With H.-J. Schneider). Adv. Math. 154, 1-45 (2000). Abstract. dvi.

Examples of self-dual Hopf algebras. (With S. Natale). J. Math. Sci. Univ. Tokyo 6, 181-215 (1999). tex . dvi. Versión publicada

Braided Hopf algebras over non-abelian groups. (With M. Graña). Bol. Acad. Nacional de Ciencias (Córdoba) 63, 45-78 (1999). dvi.

Compact quantum groups arising from the FRT construction. (With A. Abella). Bol. Acad. Nacional de Ciencias (Córdoba) 63, 15-44 (1999). pdf.

Lifting of quantum linear spaces and pointed Hopf algebras of order p³. (With H.-J. Schneider). J. Algebra 209, 658-691 (1998).

Plancherel identity for semisimple Hopf algebras. (With S. Natale). Commun. Alg. 25 (10), 3239-3254 (1997) (MR 99a:16029). pdf

Hopf algebras of order p² and braided Hopf algebras of order p. (With H.-J. Schneider). J. Algebra 199, 430-454 (1998) (MR 99c:16033).

Notas de geometría no conmutativa. Boletín Academia Nacional de Ciencias (Córdoba) vol. 61 (1995), pp. 63-82.

Compact involutions of semisimple quantum groups. Czech. J. Phys., vol. 44 (1994) pp. 963-972 (MR 96g:16050). pdf.

Notes on Extensions of Hopf algebras. Canadian J. of Math. 48 (1996), pp. 3-42 (MR 97c:16046). Appendix (With H.-J. Schneider). See here.

Extensions of Hopf algebras. (With J. Devoto). Algebra i Analiz 7, no. 1 (1995), pp. 22-61 (MR 96f:16044).

Quantum Heisenberg groups and Sklyanin algebras. (With J. Devoto and A.Tiraboschi). Letters in Math. Phys. 31, pp. 167-177, 1994. (MR 95i:17009).

Lie superbialgebras and Poisson Lie supergroups. Abh. Math. Semin. Univ. Hamb. 63, pp. 147-163, 1993 (MR 94g:17004).

Examples of compact matrix pseudogroups arising from the twisting operation. (With B. Enriquez). Commun. Math. Phys., 149, p. 195, 1992 (MR 93k:17022).

Some exceptional compact matrix pseudogroups . Bull. Soc. Math. Fr., 120, p. 297-325, 1992 (MR 93k:17023). Versión publicada

On spherical modules. In Proc. of the Third Workshop on Lie Group Repr. and its appl., Carlos Paz, 1989. (Progress in Math. 105, Birkhauser.) (MR 93i:20047).

On the realization of forms of Kac-Moody algebras. Indag. Mathem. N.S., 2(3), 275-281, 1991 (MR 93f:17036).

The representation theory of almost compact inner forms of Kac-Moody algebras. Tôhoku Math. J., vol. 43 n. 3 p. 425-445, 1991 (MR 93c:17011).

Some forms of Kac-Moody algebras. J. of Algebra vol. 147, p. 324- 344, 1992 (MR 93j: 17048). Apéndice por N. A. y G. Rousseau.

A restriction theorem for modules having a spherical submodule. (With J. Tirao). Trans. AMS, vol. 331, p. 705-725, 1992 (MR 92h:14034).

Computing some rings of invariants. Actas de la IX Esc. Latinoamer. de Matemática, Notas de Matematica Soc. Mat. Chile vol. IX, núm. 1, pp. 1-18, 1991 (MR 95f:13006).

A new proof of Tirao's Restriction Theorem. Rev. Unión Mat. Argent., Vol. 35 (dedicado al Prof. J. Rey Pastor), pp. 19-26, 1991. (MR 95a:22016).

On the Complicatedness of the pair (g, K). Rev. Mat. Univ. Complutense Madr., Vol. 2, n. 1, pp. 13-28, 1989 (MR 90b:14064). Ver comentarios de F. Knop sobre este trabajo. Versión publicada

Sur les Algèbres de polynômes graduées. C. R. Acad. Sci. Paris, t. 1308, Serie I, p. 63-65, 1989 (MR 90a:13013).

Otras publicaciones / Other articles

Mitsuhiro Takeuchi. Survey of braided Hopf algebras. New trends in Hopf algebra theory (La Falda, 1999), 301--323, Contemp. Math., 267, Amer. Math. Soc., Providence, RI, 2000. pdf

Hans-Jürgen Schneider. hanssch at rz.mathematik.uni-muenchen.de

Lectures on Hopf algebras. Trabajos de Matemática 31/95. FaMAF. pdf tex dvi.

Akira Masuoka. akira@math.tsukuba.ac.jp Foto

Extensions of Hopf algebras. Trabajos de Matemática 41/99. FaMAF. ps.

Eric Müller. eric.mueller@akdb.de

Computation of Bilinear forms. A C++ program for Nichols algebras; Documentation of the program in plain TeX.

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