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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
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
Opac: Controlla la disponibilità qui
Quantum linear groups / / Brian Parshall, Jian-pan Wang
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
Opac: Controlla la disponibilità qui
Quantum linear groups / / Brian Parshall, Jian-pan Wang
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
Opac: Controlla la disponibilità qui
Quantum linear groups / / Brian Parshall, Jian-pan Wang
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
Opac: Controlla la disponibilità qui
Representation theory : Fourth International Conference on Representation Theory, July 16-20, 2007, Lhasa, China / / Zongzhu Lin, Jianpan Wang, editors
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
Opac: Controlla la disponibilità qui
Representation theory : Fourth International Conference on Representation Theory, July 16-20, 2007, Lhasa, China / / Zongzhu Lin, Jianpan Wang, editors
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
Opac: Controlla la disponibilità qui
Representation theory : Fourth International Conference on Representation Theory, July 16-20, 2007, Lhasa, China / / Zongzhu Lin, Jianpan Wang, editors
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
Opac: Controlla la disponibilità qui