000			02772cam a22003015i 4500
001			19286115
005			20250609150035.0
008			160922s2016 nyu 000 0 eng
010			_a
020			_a9783319439303
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB27 Q6 NBHM _qCSL
100	1		_aSteinberg, Benjamin. _eauthor.
245	1	0	_aRepresentation theory of finite monoids
264		1	_aNew York : _bSpringer, _c2016.
300			_axxiv, 317 p. _c24 cm
490			_aUniversitext
520			_aThis first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modernflavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.
650			_2automata theory
650			_2finite monoids
650			_2monoid applications Markov chains
650			_2monoid applications automata theory
650			_2representation theory inverse monoids
650			_2zeta function languages
650			_2monoid algebras
942			_2CC _n0 _cTEXL _hB27 Q6 NBHM
999			_c1431519 _d1431519