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

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Bibliography 78 [Ros88] Marc Rosso. Finite-dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra. Comm. Math. Phys., 117(4):581–593, 1988. [Ros90] Marc Rosso. Analogues de la forme de Killing et du théorème d’Harish-Chandra pour les groupes quantiques. Ann. Sci. École Norm. Sup. (4), 23(3):445–467, 1990. [Ser65] Jean-Pierre Serre. Algèbre locale. Multiplicités, volume 11 of Cours au Collège de France, 1957–1958, rédigé par Pierre Gabriel. Seconde édition, 1965. Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1965. [Soĭ90] Ya. S. Soĭbel ′ man. Algebra of functions on a compact quantum group and its representations. Algebra i Analiz, 2(1):190–212, 1990. [Soi93] Yan Soibelman. Orbit method for the algebras of functions on quantum groups and coherent states. I. Internat. Math. Res. Notices, (6):151–163, 1993. [Ste68] Robert Steinberg. Lectures on Chevalley groups. Yale University, New Haven, Conn., 1968.
A Algebra with trace ........... 19 Azumaya algebra ............ 21 B Bivector field .................. 3 Bruhat decomposition ........ 16 C Characteristic polynomial .... 20 Classical double ............... 7 D Double Lie bialgebra .......... 7 Double Poisson Lie group .... 14 Dressing action .............. 15 Dual Poisson Lie group ...... 14 H Hamiltonian curve ..................... 4 vector field ................ 3 Hamiltonian derivation ........ 2 Harish Chandra homomorphism . 41 L Lie bialgebra .................. 5 M Manin triple .................. 7 Maximal order ............... 31 P Poisson affine algebraic variety .... 2 algebra ................... 2 algebraic group .......... 11 bracket ................... 2 INDEX 79 homomorphism ........... 2 manifold .................. 2 map ...................... 3 submanifold ............... 3 Q q-binomial coefficient ........ 24 q-factorial .................... 24 q-Pascal identity ............. 24 Quantum Levi factor ............... 53 unipotent subalgebra .... 53 Quantum group .............. 35 adjoint ................... 36 parabolic ................ 53 S Schubert cell ................. 17 Simple degeneration .......... 26 Symplectic leaf ....................... 4 manifold .................. 4 T Trace map ................... 19 twisted derivation ............ 25 inner .................... 25 Twisted derivation algebra ... 25 Twisted polynomial algebra .. 25
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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
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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 and 82: Bibliography 75 [DCP97] C. De Conci
Page 83: Bibliography 77 [LS91a] S. Z. Leven
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