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108 BIBLIOGRAFÍA [BG] K. A. Brown y K. R. Goodearl, Lectures on Algebraic Quantum Groups, Advanced Courses in Mathematics - CRM Barcelona. Basel: Birkhäuser. [CD] S. Caenepeel y S. Dascalescu, ‘Pointed Hopf algebras of dimension p 3 ’, J. Algebra 209 (1998), no. 2, 622–634. [Ca] E. Cartan, ‘Les groupes projectifs qui ne laissent invariante aucune multiplicité plane’, Bull. Soc. Math. France 41 (1913), 53–96. [CM] W. Chin and I. Musson, ‘The coradical filtration for quantized universal enveloping algebras’, J. London Math. Soc. 53 (1996), 50–67. [CW] A. M. Cohen y D. B. Wales, ‘Finite simple subgroups of semisimple complex Lie groups— a survey’, Groups of Lie type and their geometries (Como, 1993), 77–96, London Math. Soc. Lecture Note Ser., 207, Cambridge Univ. Press, Cambridge, 1995. [DK] C. De Concini y V. G. Kac, ‘Representations of quantum groups at roots of 1’, Operator algebras, unitary representations, enveloping algebras, and invariant theory, Proc. Colloq. in Honour of J. Dixmier, 1989 Paris/Fr. (1990) Prog. Math. 92, 471-506. [DKP] C. De Concini, V. G. Kac y C. Procesi ‘Quantum coadjoint action’, J. Am. Math. Soc. 5 (1992), no. 1, 151–189. [DL] C. De Concini y V. Lyubashenko, ‘Quantum function algebra at roots of 1’, Adv. Math. 108 (1994), no. 2, 205–262. [DT] Y. Doi y M. Takeuchi, ‘Cleft comodule algebras for a bialgebra’, Commun. Algebra 14 (1986), 801–818. [Dr] V. Drinfeld, ‘Quantum groups’, Proc. Int. Congr. Math., Berkeley 1986, Vol. 1 (1987), 798-820. [D1] [D2] [EG] [FR] E. B. Dynkin, ‘Semisimple subalgebras of semisimple Lie algebras’, Am. Math. Soc., Transl., II. Ser. 6 (1957), 111-243. E. B. Dynkin, ‘Maximal subgroups of the classical groups’, Am. Math. Soc., Transl., II. Ser. 6 (1957), 245-378. P. Etingof y S. Gelaki, ‘On families of triangular Hopf algebras’, Int. Math. Res. Not. no. 14 (2002), 757–768. W. Ferrer Santos and A. Ritatore, Actions and Invariants of Algebraic Groups. [G] G. A. García, ‘On Hopf algebras of dimension p 3 ’, Tsukuba J. Math. 29 (2005), no. 1, 259–284. [Ge1] S. Gelaki, ‘Some properties and examples of triangular pointed Hopf algebras’, Math. Res. Lett. 6 (1999), no. 5-6, 563–572. [Ge2] S. Gelaki, ‘Quantum Groups of dimension pq 2 ’, Israel J. Math. 102 (1997), 227–267. [GR] R. L. Griess Jr. y A. J. Ryba, ‘Finite simple groups which projectively embed in an exceptional Lie group are classified!’ Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 1, 75–93.
BIBLIOGRAFÍA 109 [H1] G. Hochschild, ‘Algebraic groups and Hopf algebras’, Ill. J. Math. 14 (1970), 52–65. [H2] [Hf] G. Hochschild, Basic theory of algebraic groups and Lie algebras. Graduate Texts in Mathematics, 75. Springer-Verlag, New York-Berlin, 1981. I. Hofstetter, ‘Extensions of Hopf algebras and their cohomological description’, J. Algebra 164 (1994), no. 1, 264–298. [Hu1] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, 9 (1980). New York - Heidelberg - Berlin: Springer-Verlag. XII [Hu2] J.E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, 21 (1981). New York - Heidelberg - Berlin: Springer-Verlag. XVI [J] J.C. Jantzen, Lectures on Quantum Groups, Graduate Studies in Mathematics. 6 (1996). Providence, RI: American Mathematical Society (AMS). [K] [KR] [LS] C. Kassel, Quantum Groups, Graduate Texts in Mathematics. 155 (1995). New York, NY: Springer-Verlag. L.H. Kauffman y D. Radford, ‘A necessary and sufficient condition for a finitedimensional Drinfel’d double to be a ribbon Hopf algebra’, J. Algebra 159 (1993), no.1, 98–114. R. Larson y D. Radford, ‘An associative orthogonal bilinear form for Hopf algebras’ Amer. J. Math. 91 (1969), 75–94. [LR1] R. Larson y D. Radford, ‘Semisimple cosemisimple Hopf algebras’, Amer. J. Math. 110 (1988), no. 1, 187–195. [LR2] R. Larson y D. Radford, ‘Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple’, J. Algebra 117 (1988), no. 2, 267–289. [L1] G. Lusztig, ‘Finite dimensional Hopf algebras arising from quantized universal enveloping algebras’, J. of Amer. Math. Soc. 3, 257-296. [L2] G. Lusztig, ‘Quantum groups at roots of 1’, Geom. Dedicata 35 (1990), 89-114. [L3] G. Lusztig, Introduction to quantum groups, Progress in Mathematics, 110 (1993). Birkhäuser Boston, Inc., Boston, MA. [Mj] S. Majid, ‘Crossed products by braided groups and bosonization’, J. Algebra 163 (1994), no. 1, 165–190. [MS] S. Majid and Ya. S. Soibelman, ‘Bicrossproduct structure of the quantum Weyl group’, J. Algebra 163 (1994), no. 1, 68–87. [Mk1] A. Masuoka, ‘Self dual Hopf algebras of dimension p 3 obtained by extensions’, J. Algebra 178 (1995), no. 3, 791–806. [Mk2] A. Masuoka, ‘Semisimple Hopf algebras of dimension 6, 8’, Israel. J. Math. 92 (1995), no. 1-3, 361–373.
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Álgebras de Hopf y Grupos Cuántic
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Índice general Resumen Abstract Ag
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Resumen En esta tesis discutimos al
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Abstract In this thesis we discuss
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Agradecimientos Esta tesis ha sido
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viii INTRODUCCIÓN mostró que dete
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x INTRODUCCIÓN En el Capítulo 3 d
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xii INTRODUCCIÓN Luego de estos do
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xiv INTRODUCCIÓN Finalmente, para
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Capítulo 1 Preliminares En este ca
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1.1. DEFINICIONES Y RESULTADOS BÁS
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1.2. COHOMOLOGÍA DE GRUPOS 9 lo cu
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12 CAPÍTULO 2. EXTENSIONES DE ÁLG
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28 CAPÍTULO 3. SOBRE ÁLGEBRAS DE
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Capítulo 4 Extensiones de grupos c
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4.1. ÁLGEBRAS DE COORDENADAS CUANT
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4.2. COCIENTES DE O ɛ (G) DE DIMEN
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