Theory of groups and symmetries: representations of groups and lie algebras, applications
"This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras. The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2020
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras. The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed. Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed. Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO(p, q) are studied. For this purpose, Clifford algebras in spaces R (p, q) are introduced and representations of these algebras are discussed"--Publisher's website |
| Beschreibung: | 1 Online-Ressource (xiv, 600 Seiten) |
| ISBN: | 9789811217418 |
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| 100 | 1 | |a Isaev, Alexey P. |d 1957- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Theory of groups and symmetries |b representations of groups and lie algebras, applications |c by Alexey P. Isaev, Rubakov, V. A. |
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| 520 | |a "This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras. The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed. Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed. Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO(p, q) are studied. For this purpose, Clifford algebras in spaces R (p, q) are introduced and representations of these algebras are discussed"--Publisher's website | ||
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| 650 | 4 | |a Lie algebras | |
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Datensatz im Suchindex
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| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV047124338 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:30:25Z |
| indexdate | 2024-07-10T09:03:18Z |
| institution | BVB |
| isbn | 9789811217418 |
| language | English |
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| psigel | ZDB-124-WOP |
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| publisher | World Scientific |
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| spelling | Isaev, Alexey P. 1957- Verfasser aut Theory of groups and symmetries representations of groups and lie algebras, applications by Alexey P. Isaev, Rubakov, V. A. Singapore World Scientific 2020 1 Online-Ressource (xiv, 600 Seiten) txt rdacontent c rdamedia cr rdacarrier "This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras. The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed. Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed. Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO(p, q) are studied. For this purpose, Clifford algebras in spaces R (p, q) are introduced and representations of these algebras are discussed"--Publisher's website Group theory Symmetry (Physics) Group algebras Lie algebras Rubakov, V. A. Sonstige oth https://www.worldscientific.com/worldscibooks/10.1142/11749#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Isaev, Alexey P. 1957- Theory of groups and symmetries representations of groups and lie algebras, applications Group theory Symmetry (Physics) Group algebras Lie algebras |
| title | Theory of groups and symmetries representations of groups and lie algebras, applications |
| title_auth | Theory of groups and symmetries representations of groups and lie algebras, applications |
| title_exact_search | Theory of groups and symmetries representations of groups and lie algebras, applications |
| title_exact_search_txtP | Theory of groups and symmetries representations of groups and lie algebras, applications |
| title_full | Theory of groups and symmetries representations of groups and lie algebras, applications by Alexey P. Isaev, Rubakov, V. A. |
| title_fullStr | Theory of groups and symmetries representations of groups and lie algebras, applications by Alexey P. Isaev, Rubakov, V. A. |
| title_full_unstemmed | Theory of groups and symmetries representations of groups and lie algebras, applications by Alexey P. Isaev, Rubakov, V. A. |
| title_short | Theory of groups and symmetries |
| title_sort | theory of groups and symmetries representations of groups and lie algebras applications |
| title_sub | representations of groups and lie algebras, applications |
| topic | Group theory Symmetry (Physics) Group algebras Lie algebras |
| topic_facet | Group theory Symmetry (Physics) Group algebras Lie algebras |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11749#t=toc |
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