LEADER 03517nam 22005895 450 001 9910254295303321 005 20200703092126.0 010 $a981-10-6878-X 024 7 $a10.1007/978-981-10-6878-2 035 $a(CKB)4100000001381599 035 $a(DE-He213)978-981-10-6878-2 035 $a(MiAaPQ)EBC6314845 035 $a(MiAaPQ)EBC5576560 035 $a(Au-PeEL)EBL5576560 035 $a(OCoLC)1018471569 035 $a(PPN)222226110 035 $a(EXLCZ)994100000001381599 100 $a20171229d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOn Characters of Finite Groups /$fby Michel Broué 205 $a1st ed. 2017. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2017. 215 $a1 online resource (XVI, 246 p. 9 illus., 5 illus. in color.) 225 1 $aMathematical Lectures from Peking University,$x2197-4209 311 $a981-10-6877-1 320 $aIncludes bibliographical references and index. 327 $aTensor Product.-On Representation.-Characteristic 0 representations.-Playing with the base field -- Induction, restriction -- Brauer's theorem and some applications -- Graded representations and characters -- Drinfeld Double -- Appendix A. Basics on Finite Groups -- Appendix B. Assumed results on Galois theory -- Appendix C. Integral elements -- Appendix D. Noetherian rings and modules -- Appendix E. The language of categories and functors -- Bibliography 211.-Index. 330 $aThis book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z). 410 0$aMathematical Lectures from Peking University,$x2197-4209 606 $aGroup theory 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 615 0$aGroup theory. 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 14$aGroup Theory and Generalizations. 615 24$aCategory Theory, Homological Algebra. 676 $a512.2 700 $aBroué$b Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478936 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254295303321 996 $aOn Characters of Finite Groups$91563079 997 $aUNINA