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008 111021s2012 xxu| s |||| 0|eng d
020 _a9781461407768
_9978-1-4614-0776-8
024 _a10.1007/978-1-4614-0776-8
_2doi
050 _aQA174-183
072 _aPBG
_2bicssc
072 _aMAT002010
_2bisacsh
072 _aPBG
_2thema
082 _a512.2
_223
100 _aSteinberg, Benjamin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 _aRepresentation Theory of Finite Groups
_h[electronic resource] :
_bAn Introductory Approach /
_cby Benjamin Steinberg.
250 _a1st ed. 2012.
264 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXIII, 157 p. 4 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 _aUniversitext,
_x0172-5939
520 _aRepresentation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linear algebra, group theory, and very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted. Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader. The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside's pq-theorem and the dimension theorem, permutation representations, induced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probability and statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exercises add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearly shown in diagrams. This text will engage a broad readership due to the significance of representation theory in diverse branches of mathematics, engineering, and physics, to name a few. Its primary intended use is as a one semester textbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a reference to researchers in all areas of mathematics, statistics, and several mathematical sciences.
650 _aGroup theory.
650 _aAlgebra.
650 _aGroup Theory and Generalizations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11078
650 _aAlgebra.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11000
710 _aSpringerLink (Online service)
773 _tSpringer Nature eBook
776 _iPrinted edition:
_z9781461407751
776 _iPrinted edition:
_z9781461407775
830 _aUniversitext,
_x0172-5939
856 _uhttps://doi.org/10.1007/978-1-4614-0776-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c9358
_d9358