Proceedings of the 14th International Congress on Mathematical Education : the 14th International Congress on Mathematical Education, East China Normal University, Shanghai, China, 11-18 July 2021 / / editor, Jianpan Wang |
Pubbl/distr/stampa | WSPC/ECNUP |
Disciplina | 510.71 |
Soggetto topico | Mathematics - Study and teaching |
ISBN |
9789811287169
9811287163 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Volume I -- Volume II. Invited lectures. |
Altri titoli varianti | PROCEEDINGS OF THE 14TH INTERNATIONAL CONGRESS ON MATHEMATICAL EDUCATION |
Record Nr. | UNINA-9910883693403321 |
WSPC/ECNUP | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Quantum linear groups / / Brian Parshall, Jian-pan Wang |
Autore | Parshall Brian <1945-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1991 |
Descrizione fisica | 1 online resource (168 p.) |
Disciplina | 512/.2 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Linear algebraic groups
Representations of groups Group schemes (Mathematics) |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-0862-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Introduction""; ""1. Quantum Groups""; ""1.1. Quantum affine spaces""; ""1.2. Quantum groups""; ""1.3. Direct products""; ""1.4. Closed subgroups""; ""1.5. Normal closed subgroups""; ""1.6. Kernels and exact sequences""; ""1.7. Cartesian squares""; ""1.8. Coverings""; ""2. Representation Theory of Quantum Groups""; ""2.1. Rational representations""; ""2.2. Functorial description""; ""2.3. Defining matrices""; ""2.4. Contragradient modules and tensor products""; ""2.5. Characters and character groups""; ""2.6. Fixed points""; ""2.7. Induction""; ""2.8. Injective objects""
""2.9. Exact subgroups of quantum groups""""2.10. A theorem on central faithfully flat morphisms""; ""2.11. The Hochschild-Serre spectral sequence""; ""3. Quantum Matrix Spaces""; ""3.1. Quadratic algebras""; ""3.2. Quasi-Yang-Baxter algebras""; ""3.3. Basis theorem for quasi-Yang-Baxter algebras""; ""3.4. The quadratic algebras K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)]]""; ""3.5. The quantum matrix space M[sub(q)](n)""; ""3.6. The bialgebra structure on K[M[sub(q)](n)]""; ""3.7. Some automorphisms and anti-automorphisms"" ""3.8. K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)] as K[M[sub(q)](n)]-comodules""""4. Quantum Determinants""; ""4.1. Quantum determinant""; ""4.2. First properties of the determinant""; ""4.3. Subdeterminants""; ""4.4. Laplace expansions""; ""4.5. Some commutators, I""; ""4.6. The centrality of the determinant""; ""5. The Antipode and Quantum Linear Groups""; ""5.1. Some commutators, II""; ""5.2. Some commutators, III""; ""5.3. Quantum general and special linear groups""; ""5.4. A property of the antipode""; ""6. Some Closed Subgroups""; ""6.1. Parabolic and Levi subgroups"" ""6.2. Some properties of the parabolic and Levi subgroups""""6.3. Some remarks""; ""6.4. Coadjoint action of the maximal torus and the root system""; ""6.5. Character groups of T[sub(q)] and B[sub(q)]""; ""7. Frobenius Morphisms and Kernels""; ""7.1. Gaussian polynomials""; ""7.2. Frobenius morphisms""; ""7.3. Infinitesimal subgroups""; ""7.4. Some homological properties of GL[sub(q)](n)""; ""7.5. Some exact subgroups of GL[sub(q)](n)""; ""8. Global Representation Theory""; ""8.1. Density of the ""big cell""""; ""8.2. Highest weight modules"" ""8.3. Some properties of induced G[sub(q)]-modules""""8.4. Induction to parabolic subgroups""; ""8.5. The semisimple rank 1 case, I""; ""8.6. The semisimple rank 1 case, II""; ""8.7. The one-to-one correspondence between irreducible modules and dominant weights""; ""8.8. Formal characters and their invariance under the Weyl group""; ""8.9. Injective modules for Borel subgroups""; ""8.10. A finiteness theorem; Weyl modules""; ""9. Infinitesimal Representation Theory""; ""9.1. An infinitesimal version of the ""density theorem"""" ""9.2. Highest weight and irreducible representations for (G[sub(q)])[sub(1)]-T and (G[sub(q)])[sub(1)]-B"" |
Record Nr. | UNINA-9910480335703321 |
Parshall Brian <1945-> | ||
Providence, Rhode Island : , : American Mathematical Society, , 1991 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Quantum linear groups / / Brian Parshall, Jian-pan Wang |
Autore | Parshall Brian <1945-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1991 |
Descrizione fisica | 1 online resource (168 p.) |
Disciplina | 512/.2 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Linear algebraic groups
Representations of groups Group schemes (Mathematics) |
ISBN | 1-4704-0862-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Introduction""; ""1. Quantum Groups""; ""1.1. Quantum affine spaces""; ""1.2. Quantum groups""; ""1.3. Direct products""; ""1.4. Closed subgroups""; ""1.5. Normal closed subgroups""; ""1.6. Kernels and exact sequences""; ""1.7. Cartesian squares""; ""1.8. Coverings""; ""2. Representation Theory of Quantum Groups""; ""2.1. Rational representations""; ""2.2. Functorial description""; ""2.3. Defining matrices""; ""2.4. Contragradient modules and tensor products""; ""2.5. Characters and character groups""; ""2.6. Fixed points""; ""2.7. Induction""; ""2.8. Injective objects""
""2.9. Exact subgroups of quantum groups""""2.10. A theorem on central faithfully flat morphisms""; ""2.11. The Hochschild-Serre spectral sequence""; ""3. Quantum Matrix Spaces""; ""3.1. Quadratic algebras""; ""3.2. Quasi-Yang-Baxter algebras""; ""3.3. Basis theorem for quasi-Yang-Baxter algebras""; ""3.4. The quadratic algebras K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)]]""; ""3.5. The quantum matrix space M[sub(q)](n)""; ""3.6. The bialgebra structure on K[M[sub(q)](n)]""; ""3.7. Some automorphisms and anti-automorphisms"" ""3.8. K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)] as K[M[sub(q)](n)]-comodules""""4. Quantum Determinants""; ""4.1. Quantum determinant""; ""4.2. First properties of the determinant""; ""4.3. Subdeterminants""; ""4.4. Laplace expansions""; ""4.5. Some commutators, I""; ""4.6. The centrality of the determinant""; ""5. The Antipode and Quantum Linear Groups""; ""5.1. Some commutators, II""; ""5.2. Some commutators, III""; ""5.3. Quantum general and special linear groups""; ""5.4. A property of the antipode""; ""6. Some Closed Subgroups""; ""6.1. Parabolic and Levi subgroups"" ""6.2. Some properties of the parabolic and Levi subgroups""""6.3. Some remarks""; ""6.4. Coadjoint action of the maximal torus and the root system""; ""6.5. Character groups of T[sub(q)] and B[sub(q)]""; ""7. Frobenius Morphisms and Kernels""; ""7.1. Gaussian polynomials""; ""7.2. Frobenius morphisms""; ""7.3. Infinitesimal subgroups""; ""7.4. Some homological properties of GL[sub(q)](n)""; ""7.5. Some exact subgroups of GL[sub(q)](n)""; ""8. Global Representation Theory""; ""8.1. Density of the ""big cell""""; ""8.2. Highest weight modules"" ""8.3. Some properties of induced G[sub(q)]-modules""""8.4. Induction to parabolic subgroups""; ""8.5. The semisimple rank 1 case, I""; ""8.6. The semisimple rank 1 case, II""; ""8.7. The one-to-one correspondence between irreducible modules and dominant weights""; ""8.8. Formal characters and their invariance under the Weyl group""; ""8.9. Injective modules for Borel subgroups""; ""8.10. A finiteness theorem; Weyl modules""; ""9. Infinitesimal Representation Theory""; ""9.1. An infinitesimal version of the ""density theorem"""" ""9.2. Highest weight and irreducible representations for (G[sub(q)])[sub(1)]-T and (G[sub(q)])[sub(1)]-B"" |
Record Nr. | UNINA-9910788874703321 |
Parshall Brian <1945-> | ||
Providence, Rhode Island : , : American Mathematical Society, , 1991 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Quantum linear groups / / Brian Parshall, Jian-pan Wang |
Autore | Parshall Brian <1945-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1991 |
Descrizione fisica | 1 online resource (168 p.) |
Disciplina | 512/.2 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Linear algebraic groups
Representations of groups Group schemes (Mathematics) |
ISBN | 1-4704-0862-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Introduction""; ""1. Quantum Groups""; ""1.1. Quantum affine spaces""; ""1.2. Quantum groups""; ""1.3. Direct products""; ""1.4. Closed subgroups""; ""1.5. Normal closed subgroups""; ""1.6. Kernels and exact sequences""; ""1.7. Cartesian squares""; ""1.8. Coverings""; ""2. Representation Theory of Quantum Groups""; ""2.1. Rational representations""; ""2.2. Functorial description""; ""2.3. Defining matrices""; ""2.4. Contragradient modules and tensor products""; ""2.5. Characters and character groups""; ""2.6. Fixed points""; ""2.7. Induction""; ""2.8. Injective objects""
""2.9. Exact subgroups of quantum groups""""2.10. A theorem on central faithfully flat morphisms""; ""2.11. The Hochschild-Serre spectral sequence""; ""3. Quantum Matrix Spaces""; ""3.1. Quadratic algebras""; ""3.2. Quasi-Yang-Baxter algebras""; ""3.3. Basis theorem for quasi-Yang-Baxter algebras""; ""3.4. The quadratic algebras K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)]]""; ""3.5. The quantum matrix space M[sub(q)](n)""; ""3.6. The bialgebra structure on K[M[sub(q)](n)]""; ""3.7. Some automorphisms and anti-automorphisms"" ""3.8. K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)] as K[M[sub(q)](n)]-comodules""""4. Quantum Determinants""; ""4.1. Quantum determinant""; ""4.2. First properties of the determinant""; ""4.3. Subdeterminants""; ""4.4. Laplace expansions""; ""4.5. Some commutators, I""; ""4.6. The centrality of the determinant""; ""5. The Antipode and Quantum Linear Groups""; ""5.1. Some commutators, II""; ""5.2. Some commutators, III""; ""5.3. Quantum general and special linear groups""; ""5.4. A property of the antipode""; ""6. Some Closed Subgroups""; ""6.1. Parabolic and Levi subgroups"" ""6.2. Some properties of the parabolic and Levi subgroups""""6.3. Some remarks""; ""6.4. Coadjoint action of the maximal torus and the root system""; ""6.5. Character groups of T[sub(q)] and B[sub(q)]""; ""7. Frobenius Morphisms and Kernels""; ""7.1. Gaussian polynomials""; ""7.2. Frobenius morphisms""; ""7.3. Infinitesimal subgroups""; ""7.4. Some homological properties of GL[sub(q)](n)""; ""7.5. Some exact subgroups of GL[sub(q)](n)""; ""8. Global Representation Theory""; ""8.1. Density of the ""big cell""""; ""8.2. Highest weight modules"" ""8.3. Some properties of induced G[sub(q)]-modules""""8.4. Induction to parabolic subgroups""; ""8.5. The semisimple rank 1 case, I""; ""8.6. The semisimple rank 1 case, II""; ""8.7. The one-to-one correspondence between irreducible modules and dominant weights""; ""8.8. Formal characters and their invariance under the Weyl group""; ""8.9. Injective modules for Borel subgroups""; ""8.10. A finiteness theorem; Weyl modules""; ""9. Infinitesimal Representation Theory""; ""9.1. An infinitesimal version of the ""density theorem"""" ""9.2. Highest weight and irreducible representations for (G[sub(q)])[sub(1)]-T and (G[sub(q)])[sub(1)]-B"" |
Record Nr. | UNINA-9910827438403321 |
Parshall Brian <1945-> | ||
Providence, Rhode Island : , : American Mathematical Society, , 1991 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Representation theory : Fourth International Conference on Representation Theory, July 16-20, 2007, Lhasa, China / / Zongzhu Lin, Jianpan Wang, editors |
Autore | Vasilʹev V. A. <1956-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
Descrizione fisica | 1 online resource (314 p.) |
Disciplina | 514.24 |
Collana | Contemporary mathematics |
Soggetto topico |
Representations of algebras
Representations of groups |
ISBN |
0-8218-8157-4
0-8218-5806-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Characters of simply laced nonconnected groups versus characters of non-simply laced connected groups -- Classification of finite-dimensional basic Hopf algebras according to their representation type -- 1. Introduction -- 2. Representation type of basic Hopf algebras -- 3. Classification of basic Hopf algebras of finite representation type -- 4. Classification of basic Hopf algebras of tame type -- Acknowledgement -- References -- Twelve bridges from a reductive group to its Langlands dual -- Some new highest weight categories. |
Record Nr. | UNINA-9910788796503321 |
Vasilʹev V. A. <1956-> | ||
Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Representation theory : Fourth International Conference on Representation Theory, July 16-20, 2007, Lhasa, China / / Zongzhu Lin, Jianpan Wang, editors |
Autore | Vasilʹev V. A. <1956-> |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
Descrizione fisica | 1 online resource (314 p.) |
Disciplina | 514.24 |
Collana | Contemporary mathematics |
Soggetto topico |
Representations of algebras
Representations of groups |
ISBN |
0-8218-8157-4
0-8218-5806-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Characters of simply laced nonconnected groups versus characters of non-simply laced connected groups -- Classification of finite-dimensional basic Hopf algebras according to their representation type -- 1. Introduction -- 2. Representation type of basic Hopf algebras -- 3. Classification of basic Hopf algebras of finite representation type -- 4. Classification of basic Hopf algebras of tame type -- Acknowledgement -- References -- Twelve bridges from a reductive group to its Langlands dual -- Some new highest weight categories. |
Record Nr. | UNINA-9910808663903321 |
Vasilʹev V. A. <1956-> | ||
Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Representation theory : Fourth International Conference on Representation Theory, July 16-20, 2007, Lhasa, China / / Zongzhu Lin, Jianpan Wang, editors |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
Descrizione fisica | 1 online resource (314 p.) |
Disciplina | 514.24 |
Collana | Contemporary mathematics |
Soggetto topico |
Representations of algebras
Representations of groups |
Soggetto genere / forma | Electronic books. |
ISBN |
0-8218-8157-4
0-8218-5806-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups""""Classification of finite-dimensional basic Hopf algebras according to their representation type""; ""1. Introduction""; ""2. Representation type of basic Hopf algebras""; ""3. Classification of basic Hopf algebras of finite representation type""; ""4. Classification of basic Hopf algebras of tame type""; ""Acknowledgement""; ""References""; ""Twelve bridges from a reductive group to its Langlands dual""; ""Some new highest weight categories"" |
Record Nr. | UNINA-9910480164603321 |
Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|