000 02249cam a2200277 i 4500
001 20435139
005 20250611103941.0
008 180406t20182018riua b 001 0 eng
020 _a9781470436803
040 _aCSL
_cCSL
041 _2eng
_aeng
084 _aB27M09 Q8 NBHM
_qCSL
100 1 _aLorenz, Martin,
_eauthor.
_9812548
245 1 2 _aTour of representation theory
264 1 _aProvidence :
_bAmerican Mathematical Society,
_c2018.
300 _axvii, 654 p. :
_bill. ;
_c27 cm.
490 0 _aGraduate studies in mathematics ;
_v193
504 _aIncludes bibliographical references and indexes.
520 _aRepresentation theory investigates the different ways in which a given algebraic object—such as a group or a Lie algebra—can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.
650 0 _aRepresentations of groups.
_9714562
650 0 _aRepresentations of algebras.
_9812549
650 0 _aRepresentations of Lie algebras.
_9812550
650 0 _aVector spaces.
_9715317
650 0 _aCategories (Mathematics)
_9812551
942 _2CC
_n0
_cTEXL
_hB27M09 Q8 NBHM
999 _c1431592
_d1431592