LEADER 05944nam 22006732 450 001 9910454946603321 005 20151005020622.0 010 $a1-107-12542-1 010 $a1-139-63692-8 010 $a1-283-87103-3 010 $a1-139-81164-9 010 $a0-511-04524-7 010 $a0-511-81453-4 010 $a0-511-15478-X 010 $a0-511-01700-6 035 $a(CKB)111056485655768 035 $a(EBL)202084 035 $a(OCoLC)808028315 035 $a(UkCbUP)CR9780511814532 035 $a(MiAaPQ)EBC202084 035 $a(Au-PeEL)EBL202084 035 $a(CaPaEBR)ebr10006823 035 $a(CaONFJC)MIL418353 035 $a(EXLCZ)99111056485655768 100 $a20101021d2001|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRepresentations and characters of groups /$fGordon James and Martin Liebeck$b[electronic resource] 205 $aSecond edition. 210 1$aCambridge :$cCambridge University Press,$d2001. 215 $a1 online resource (viii, 458 pages) $cdigital, PDF file(s) 225 1 $aCambridge mathematical textbooks 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-00392-X 311 $a0-521-81205-4 320 $aIncludes bibliographical references (p. 454) and index. 327 $aCover; Half-title; Title; Copyright; Contents; Preface; 1 Groups and homomorphisms; Groups; 1.1 Examples; Subgroups; 1.2 Examples; Direct products; 1.3 Example; Functions; Homomorphisms; 1.4 Example; 1.5 Example; Cosets; 1.6 Lagrange's Theorem; Normal subgroups; 1.7 Examples; Simple groups; Kernels and images; (1.8); (1.9); 1.10 Theorem; 1.11 Example; Summary of Chapter 1; Exercises for Chapter 1; 2 Vector spaces and linear transformations; Vector spaces; (2.1); 2.2 Examples; Bases of vector spaces; 2.3 Example; (2.4); Subspaces; (2.5); 2.6 Examples; (2.7); Direct sums of subspaces 327 $a2.8 Examples(2.9); (2.10); Linear transformations; Kernels and images; (2:11); (2:12); 2.13 Examples; Invertible linear transformations; (2.14); Endomorphisms; (2.15); 2.16 Examples; Matrices; 2.17 Definition; 2.18 Examples; 2.19 Example; (2.20); (2.21); 2.22 Example; Invertible matrices; 2.23 Definition; (2.24); 2.25 Example; Eigenvalues; (2.26); 2.27 Examples; 2.28 Example; Projections; 2.29 Proposition; 2.30 Definition; 2.31 Example; 2.32 Proposition; 2.33 Example; Summary of Chapter 2; Exercises for Chapter 2; 3 Group representations; Representations; 3.1 Definition; 3.2 Examples 327 $aEquivalent representations3.3 Definition; 3.4 Examples; Kernels of representations; 3.5 Definition; 3.6 Definition; 3.7 Proposition; 3.8 Examples; Summary of Chapter 3; Exercises for Chapter 3; 4 FG-modules; FG-modules; 4.1 Example; 4.2 Definition; 4.3 Definition; 4.4 Theorem; 4.5 Examples; 4.6 Proposition; (4.7); 4.8 Definitions; Permutation modules; 4.9 Example; 4.10 Definition; 4.11 Example; FG-modules and equivalent representations; 4.12 Theorem; 4.13 Example; Summary of Chapter 4; Exercises for Chapter 4; 5 FG-submodules and reducibility; FG-submodules; 5.1 Definition; 5.2 Examples 327 $aIrreducible FG-modules5.3 Definition; (5.4); 5.5 Examples; Summary of Chapter 5; Exercises for Chapter 5; 6 Group algebras; The group algebra of G; 6.1 Example; 6.2 Example; 6.3 Definition; 6.4 Proposition; The regular FG-module; 6.5 Definition; 6.6 Proposition; 6.7 Example; FG acts on an FG-module; 6.8 Definition; 6.9 Examples; 6.10 Proposition; Summary of Chapter 6; Exercises for Chapter 6; 7 FG-homomorphisms; FG-homomorphisms; 7.1 Definition; 7.2 Proposition; 7.3 Examples; Isomorphic FG-modules; 7.4 Definition; 7.5 Proposition; 7.6 Theorem; (7.7); 7.8 Example; 7.9 Example; Direct sums 327 $a(7.10)7.11 Proposition; 7.12 Proposition; Summary of Chapter 7; Exercises for Chapter 7; 8 Maschke's Theorem; Maschke's Theorem; 8.1 Maschke's Theorem; 8.2 Examples; (8.3); (8.4); 8.5 Example; Consequences of Maschke's Theorem; 8.6 Definition; 8.7 Theorem; 8.8 Proposition; Summary of Chapter 8; Exercises for Chapter 8; 9 Schur's Lemma; Schur's Lemma; 9.1 Schur's Lemma; 9.2 Proposition; 9.3 Corollary; 9.4 Examples; Reprensentation theory of finite abelian groups; 9.5 Proposition; 9.6 Theorem; (9.7); 9.8 Theorem; 9.9 Examples; Diagonalization; (9.10); 9.11 Proposition 327 $aSome further applications of Schur's Lemma 330 $aThis book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians. 410 0$aCambridge mathematical textbooks 517 3 $aRepresentations & Characters of Groups 606 $aRepresentations of groups 615 0$aRepresentations of groups. 676 $a512/.2 700 $aJames$b G. D$g(Gordon Douglas),$f1945-$01051717 702 $aLiebeck$b M. W$g(Martin W.),$f1954- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910454946603321 996 $aRepresentations and characters of groups$92482434 997 $aUNINA LEADER 01962oam 2200565 450 001 9910706568503321 005 20171122090526.0 035 $a(CKB)5470000002456761 035 $a(OCoLC)892425141 035 $a(OCoLC)995470000002456761 035 $a(EXLCZ)995470000002456761 100 $a20141006d1960 ua 0 101 0 $aeng 135 $aurmn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTrepostomatous Bryozoa of the Hamilton group of New York State /$fby Richard S. Boardman 210 1$aWashington :$cUnited States Department of the Interior, Geological Survey,$d1960. 215 $a1 online resource (iii, 87 pages, 22 unnumbered pages of plates) $cillustrations, maps 225 1 $aGeological Survey professional paper ;$v340 300 $aTitle from title screen (viewed September 30, 2014). 300 $a"Geology, evolution, and descriptions, based on a revised method of classification." 320 $aIncludes bibliographical references (pages 82-83) and index. 606 $aBryozoa, Fossil$zNew York (State) 606 $aPaleontology$yDevonian 606 $aPaleontology$zNew York (State) 606 $aTrepostomata$zNew York (State) 606 $aDevonian Geologic Period$2fast 606 $aPaleontology$2fast 606 $aTrepostomata$2fast 607 $aNew York (State)$2fast 615 0$aBryozoa, Fossil 615 0$aPaleontology 615 0$aPaleontology 615 0$aTrepostomata 615 7$aDevonian Geologic Period. 615 7$aPaleontology. 615 7$aTrepostomata. 700 $aBoardman$b Richard S.$01399266 712 02$aGeological Survey (U.S.), 801 0$bCOP 801 1$bCOP 801 2$bOCLCO 801 2$bOCLCF 801 2$bGPO 906 $aBOOK 912 $a9910706568503321 996 $aTrepostomatous Bryozoa of the Hamilton group of New York State$93464163 997 $aUNINA