Degree of Parabolic Quantum Groups - Dipartimento di Matematica ...

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Bibliography 76 [HL94] Timothy J. Hodges and Thierry Levasseur. Primitive ideals of Cq[SL(n)]. J. Algebra, 168(2):455–468, 1994. [Hum78] James E. Humphreys. Introduction to Lie algebras and representation theory, volume 9 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1978. [Jim85] Michio Jimbo. A q-difference analogue of U(g) and the Yang- Baxter equation. Lett. Math. Phys., 10(1):63–69, 1985. [Jim86a] Michio Jimbo. A q-analogue of U(gl(N +1)), Hecke algebra, and the Yang-Baxter equation. Lett. Math. Phys., 11(3):247–252, 1986. [Jim86b] Michio Jimbo. Quantum R matrix for the generalized Toda system. Comm. Math. Phys., 102(4):537–547, 1986. [Jim86c] Michio Jimbo. Quantum R matrix related to the generalized Toda system: an algebraic approach. In Field theory, quantum gravity and strings (Meudon/Paris, 1984/1985), volume 246 of Lecture Notes in Phys., pages 335–361. Springer, Berlin, 1986. [Jos95] Anthony Joseph. Quantum groups and their primitive ideals, volume 29 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Springer-Verlag, Berlin, 1995. [Kac90] Victor G. Kac. Infinite-dimensional Lie algebras. Cambridge University Press, Cambridge, 1990. [Kas95] Christian Kassel. Quantum groups, volume 155 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. [KL91] David Kazhdan and George Lusztig. Affine Lie algebras and quantum groups. Internat. Math. Res. Notices, (2):21–29, 1991. [Kna02] Anthony W. Knapp. Lie groups beyond an introduction, volume 140 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, 2002. [KS98] Leonid I. Korogodski and Yan S. Soibelman. Algebras of functions on quantum groups. Part I, volume 56 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1998. [KW76] V. Kac and B. Weisfeiler. Coadjoint action of a semi-simple algebraic group and the center of the enveloping algebra in characteristic p. Nederl. Akad. Wetensch. Proc. Ser. A 79=Indag. Math., 38(2):136–151, 1976.
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Università degli studi Roma Tre Do
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Contents ii Part II Quantum Groups
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Contents iv there exists a non empt
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Part I USEFUL ALGEBRAIC AND GEOMETR
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1. Poisson algebraic Groups 3 Defin
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1. Poisson algebraic Groups 5 1.2 L
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1. Poisson algebraic Groups 7 1.2.2
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1. Poisson algebraic Groups 9 Examp
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1. Poisson algebraic Groups 11 1.3
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1. Poisson algebraic Groups 13 Exam
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Proof. See [KS98], page 23. Proposi
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1. Poisson algebraic Groups 17 Let
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2. ALGEBRAS WITH TRACE In this chap
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2. Algebras with trace 21 Example 2
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3. TWISTED POLYNOMIAL ALGEBRAS In t
Page 31 and 32: 3. Twisted polynomial algebras 25 3
Page 33 and 34: 3. Twisted polynomial algebras 27 3
Page 35 and 36: 3. Twisted polynomial algebras 29 (
Page 37 and 38: 3. Twisted polynomial algebras 31 m
Page 39 and 40: 3. Twisted polynomial algebras 33 P
Page 41 and 42: 4. GENERAL THEORY We briefly recall
Page 43 and 44: 4. General Theory 37 Now we use the
Page 45 and 46: subject to the following relations:
Page 47 and 48: 4. General Theory 41 4.2.1 The cent
Page 49 and 50: 4. General Theory 43 For α ∈ R +
Page 51 and 52: 4. General Theory 45 Let G be the c
Page 53 and 54: Theorem 4.4.1. Uǫ is a maximal ord
Page 55 and 56: 4. General Theory 49 Thus we introd
Page 57 and 58: 5. QUANTUM UNIVERSAL ENVELOPING ALG
Page 59 and 60: 5. Quantum universal enveloping alg
Page 79 and 80: BIBLIOGRAPHY [Abe80] Eiichi Abe. Ho
Page 81: Bibliography 75 [DCP97] C. De Conci
Page 85: A Algebra with trace ........... 19
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