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[null,"1.","Record Nr.",null,"UNINA9910788874703321"]
[null,null,"Autore",null,"Parshall Brian <1945->"]
[null,null,"Titolo",null,"Quantum linear groups / / Brian Parshall, Jian-pan Wang"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , 1991"]
[{"$nulls":4},"©1991"]
[null,null,"ISBN",null,"1-4704-0862-7"]
[null,null,"Descrizione fisica",null,"1 online resource (168 p.)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 439"]
[null,null,"Disciplina",null,"512/.2"]
[null,null,"Soggetti",null,"Linear algebraic groups"]
[{"$nulls":4},"Representations of groups"]
[{"$nulls":4},"Group schemes (Mathematics)"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"January 1991, Volume 89, Number 439 (second of 3 numbers).\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"\"\"Contents\"\"; \"\"Introduction\"\"; \"\"1. Quantum Groups\"\"; \"\"1.1. Quantum affine spaces\"\"; \"\"1.2. Quantum groups\"\"; \"\"1.3. Direct products\"\"; \"\"1.4. Closed subgroups\"\"; \"\"1.5. Normal closed subgroups\"\"; \"\"1.6. Kernels and exact sequences\"\"; \"\"1.7. Cartesian squares\"\"; \"\"1.8. Coverings\"\"; \"\"2. Representation Theory of Quantum Groups\"\"; \"\"2.1. Rational representations\"\"; \"\"2.2. Functorial description\"\"; \"\"2.3. Defining matrices\"\"; \"\"2.4. Contragradient modules and tensor products\"\"; \"\"2.5. Characters and character groups\"\"; \"\"2.6. Fixed points\"\"; \"\"2.7. Induction\"\"; \"\"2.8. Injective objects\"\""]
[{"$nulls":4},"\"\"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(nâ€Œ0)][sub(q)]] and K[A[sup(nâ€Œ0)][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\"\""]
[{"$nulls":4},"\"\"3.8. K[A[sup(nâ€Œ0)][sub(q)]] and K[A[sup(nâ€Œ0)][sub(q)] as K[M[sub(q)](n)]-comodules\"\"\"\"4. Quantum Determinants\"\"; \"\"4.1. Quantum determinant\"\"; \"\"4.2. First properties of the determinant\"\"; \"\"4.3. Subdeterminants\"\"; \"\"4.4. Laplace expansions\"\"; \"\"4.5. Some commutators, I\"\"; \"\"4.6. The centrality of the determinant\"\"; \"\"5. The Antipode and Quantum Linear Groups\"\"; \"\"5.1. Some commutators, II\"\"; "]
[{"$nulls":4},"\"\"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\"\""]
[{"$nulls":4},"\"\"6.2. Some properties of the parabolic and Levi subgroups\"\"\"\"6.3. Some remarks\"\"; \"\"6.4. Coadjoint action of the maximal torus and the root system\"\"; \"\"6.5. Character groups of T[sub(q)] and B[sub(q)]\"\"; \"\"7. Frobenius Morphisms and Kernels\"\"; \"\"7.1. Gaussian polynomials\"\"; \"\"7.2. Frobenius morphisms\"\"; \"\"7.3. Infinitesimal subgroups\"\"; \"\"7.4. Some homological properties of GL[sub(q)](n)\"\"; \"\"7.5. Some exact subgroups of GL[sub(q)](n)\"\"; \"\"8. Global Representation Theory\"\"; \"\"8.1. Density of the \"\"big cell\"\"\"\"; \"\"8.2. Highest weight modules\"\""]
[{"$nulls":4},"\"\"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\"\"\"\""]
[{"$nulls":4},"\"\"9.2. Highest weight and irreducible representations for (G[sub(q)])[sub(1)]-T and (G[sub(q)])[sub(1)]-B\"\""]