國立虎尾科技大學 |

Theory of groups and symmetries = representations of groups and lie algebras, applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Theory of groups and symmetries/ Alexey P. Isaev, V. Aalery A. Rubakov.
其他題名:	representations of groups and lie algebras, applications /
作者:	Isaev, Alexey P.,
其他作者:	Rubakov, V. A.
出版者:	Singapore :World Scientific, : c2021.,
面頁冊數:	1 online resource (xiv, 600 p.)
標題:	Lie algebras. -
電子資源:	https://www.worldscientific.com/worldscibooks/10.1142/11749#t=toc
ISBN:	9789811217418

Theory of groups and symmetries = representations of groups and lie algebras, applications /
Isaev, Alexey P.,1957-

Theory of groups and symmetriesrepresentations of groups and lie algebras, applications /[electronic resource] :Alexey P. Isaev, V. Aalery A. Rubakov. - 1st ed. - Singapore :World Scientific,c2021. - 1 online resource (xiv, 600 p.)

Includes bibliographical references and index.

"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.

Mode of access: World Wide Web.

ISBN: 9789811217418Subjects--Topical Terms:

527930
Lie algebras.

LC Class. No.: QC20.7.G76 / I84 2020

Dewey Class. No.: 512.2

Theory of groups and symmetries = representations of groups and lie algebras, applications /
LDR:02702cam a2200289 a 4500 001 1042288
003 WSP
006 m o d
007 cr cnu---unuuu
008 211216s2021 si ob 001 0 eng d
010 $z 2020019144
020 $a 9789811217418 $q (ebook)
020 $a 9789811217425 $q (ebook)
020 $z 9789811217401 $q (hbk.)
035 $a 00011749
040 $a WSPC $b eng $c WSPC
050 0 4 $a QC20.7.G76 $b I84 2020
082 0 4 $a 512.2 $2 23
100 1 $a Isaev, Alexey P., $d 1957- $3 1342559
245 1 0 $a Theory of groups and symmetries $h [electronic resource] : $b representations of groups and lie algebras, applications / $c Alexey P. Isaev, V. Aalery A. Rubakov.
250 $a 1st ed.
260 $a Singapore : $b World Scientific, $c c2021.
300 $a 1 online resource (xiv, 600 p.)
504 $a Includes bibliographical references and index.
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.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Description based on print version record.
650 0 $a Lie algebras. $3 527930
650 0 $a Group algebras. $3 905294
650 0 $a Symmetry (Physics) $3 591962
650 0 $a Group theory. $3 527791
700 1 $a Rubakov, V. A. $3 856865
856 4 0 $u https://www.worldscientific.com/worldscibooks/10.1142/11749#t=toc