TY  - BOOK
AU  - Yakimov,Milen
TI  - On the Spectra of Quantum Groups
T2  - Memoirs of the American Mathematical Society
SN  - 9781470415327
AV  - QC174.17.G7 -- .Y35 2013eb 
U1  - 530.14/3 
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Quantum groups
KW  - Electronic books
N1  - Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Previous results on spectra of quantum function algebras -- 2.1. Quantized universal enveloping algebras -- 2.2. Type 1 modules and braid group action -- 2.3.   -prime ideals of Quantum Groups -- 2.4. Sets of normal elements -- 2.5. Localizations of quotients of   _{  }[  ] by its   -primes -- 2.6. Spectral decomposition theorem for   _{  }[  ] -- 2.7. The De Concini-Kac-Procesi algebras -- 2.8. A second presentation of   ^{  }_{±} -- Chapter 3. A description of the centers of Joseph's localizations -- 3.1. Statement of the main result -- 3.2. Associated root and weight spaces -- 3.3. One side inclusion in \thref{BFW-CENTER} -- 3.4. Joseph's description of   _{  } -- 3.5. Homogeneous   -normal elements of the algebras   ^{±}_{  _{±}} -- 3.6. Homogeneous   -normal elements of the algebras   _{  } -- 3.7. Proof of \thref{BFW-CENTER} -- Chapter 4. Primitive ideals of   _{  }[  ] and a Dixmier map for   _{  }[  ] -- 4.1. A formula for the primitive ideals of   _{  }[  ] -- 4.2. Structure of         _{  }  _{  }[  ] as a   ^{  }×  ^{  }-homogeneous space -- 4.3. The standard Poisson Lie structure on    and its symplectic leaves -- 4.4. Equations for the symplectic leaves of (  ^{  },  _{  }) -- 4.5. A   ^{  }×  ^{  }-equivariant Dixmier map for ℝ_{  }[  ] -- Chapter 5. Separation of variables for the algebras   ^{±}_{  } -- 5.1. Statement of the freeness result -- 5.2. Leading terms of the normal elements   _{  }^{±}(  ^{±}_{  ,  }) -- 5.3. Proof of \thref{FREES} -- Chapter 6. A classification of the normal and prime elements of the De Concini-Kac-Procesi algebras -- 6.1. Statement of the classification result -- 6.2. Homogeneous normal and   -normal elements of   ^{±}_{  } -- 6.3. A lemma on diagonal automorphisms of   ^{  }_{±} -- 6.4. Proof of \prref{NORMALP}; 6.5. Proof of \thref{NORMAL1} -- 6.6. Prime and primitive ideals in the {0}-stratum of           ^{±}_{  }. -- 6.7. A classification of the prime elements of   ^{±}_{  } -- Chapter 7. Module structure of   _{  } over their subalgebras generated by Joseph's normal elements -- 7.1. Statement of the freeness result -- 7.2. A   ×  -filtration of   _{  } -- 7.3. The action of       '_{  } on       _{  } -- 7.4. Structure of the algebras   '_{  } and separation of variables for   _{  } -- 7.5. Structure of the algebras   _{  } and freeness of   _{  } over   _{  } -- Chapter 8. A classification of maximal ideals of   _{  }[  ] and a question of Goodearl and Zhang -- 8.1. A projection property of the ideal   _{(1,1)} -- 8.2. Proof of \prref{PROJJ} -- 8.3. Proof of \thref{MAX} -- 8.4. Classification of         _{  }[  ] and a question of Goodearl and Zhang -- Chapter 9. Chain properties and homological applications -- 9.1. Applications -- 9.2.   ⁺⊛  ⁻ is an algebra with enough normal elements. -- Bibliography
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114051
ER  -