Teoria de representação

Teoria de representação é um campo da matemática que estuda estruturas algébricas abstratas pela representação de seus elementos como transformações lineares de espaços vetoriais.^[1]

Referências

↑ Textos clássicos sobre teoria da representação incluem Curtis & Reiner (1962) e Serre (1977). Outras fontes excelentes são Fulton & Harris (1991) e Goodman & Wallach (1998).

Bibliografia

Alperin, J. L. (1986), Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups, ISBN 978-0-521-44926-7, Cambridge University Press .
Bargmann, V. (1947), «Irreducible unitary representations of the Lorenz group», Annals of Mathematics, 48 (3): 568–640, JSTOR 1969129, doi:10.2307/1969129 .
Borel, Armand (2001), Essays in the History of Lie Groups and Algebraic Groups, ISBN 978-0-8218-0288-5, American Mathematical Society .
Borel, Armand; Casselman, W. (1979), Automorphic Forms, Representations, and L-functions, ISBN 978-0-8218-1435-2, American Mathematical Society .
Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, ISBN 978-0-470-18975-7, John Wiley & Sons (Reedition 2006 by AMS Bookstore) .
Gelbart, Stephen (1984), «An Elementary Introduction to the Langlands Program», Bulletin of the American Mathematical Society, 10 (2): 177–219, doi:10.1090/S0273-0979-1984-15237-6 .
Folland, Gerald B. (1995), A Course in Abstract Harmonic Analysis, ISBN 978-0-8493-8490-5, CRC Press .
Fulton, William; Harris, Joe (1991). Representation theory. A first course. Col: Graduate Texts in Mathematics, Readings in Mathematics (em inglês). 129. New York: Springer-Verlag. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103. doi:10.1007/978-1-4612-0979-9
Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, ISBN 978-0-521-66348-9, Cambridge University Press .
James, Gordon; Liebeck, Martin (1993), Representations and Characters of Groups, ISBN 978-0-521-44590-0, Cambridge: Cambridge University Press .
Hall, Brian C. (2015), Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, ISBN 978-3319134666, Graduate Texts in Mathematics, 222 2nd ed. , Springer
Helgason, Sigurdur (1978), Differential Geometry, Lie groups and Symmetric Spaces, ISBN 978-0-12-338460-7, Academic Press
Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, ISBN 978-0-387-90053-7, Birkhäuser .
Humphreys, James E. (1972b), Linear Algebraic Groups, ISBN 978-0-387-90108-4, Graduate Texts in Mathematics, 21, Berlin, New York: Springer-Verlag, MR 0396773
Jantzen, Jens Carsten (2003), Representations of Algebraic Groups, ISBN 978-0-8218-3527-2, American Mathematical Society .
Kac, Victor G. (1977), «Lie superalgebras», Advances in Mathematics, 26 (1): 8–96, doi:10.1016/0001-8708(77)90017-2 .
Kac, Victor G. (1990), Infinite Dimensional Lie Algebras, ISBN 978-0-521-46693-6 3rd ed. , Cambridge University Press .
Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, ISBN 978-0-691-09089-4, Princeton University Press .
Kim, Shoon Kyung (1999), Group Theoretical Methods and Applications to Molecules and Crystals: And Applications to Molecules and Crystals, ISBN 978-0-521-64062-6, Cambridge University Press .
Kostrikin, A. I.; Manin, Yuri I. (1997), Linear Algebra and Geometry, ISBN 978-90-5699-049-7, Taylor & Francis .
Lam, T. Y. (1998), «Representations of finite groups: a hundred years», Notices of the AMS, 45 (3,4): 361–372 (Part I), 465–474 (Part II) .
Yurii I. Lyubich. Introduction to the Theory of Banach Representations of Groups. Translated from the 1985 Russian-language edition (Kharkov, Ukraine). Birkhäuser Verlag. 1988.
Mumford, David; Fogarty, J.; Kirwan, F. (1994), Geometric invariant theory, ISBN 978-3-540-56963-3, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], 34 3rd ed. , Berlin, New York: Springer-Verlag, MR 0214602 ; MR 0719371 (2nd ed.); MR 1304906(3rd ed.)
Olver, Peter J. (1999), Classical invariant theory, ISBN 978-0-521-55821-1, Cambridge: Cambridge University Press .
Peter, F.; Weyl, Hermann (1927), «Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe», Mathematische Annalen, 97 (1): 737–755, doi:10.1007/BF01447892, arquivado do original em 19 de agosto de 2014 .
Pontrjagin, Lev S. (1934), «The theory of topological commutative groups», Annals of Mathematics, 35 (2): 361–388, JSTOR 1968438, doi:10.2307/1968438 .
Sally, Paul; Vogan, David A. (1989), Representation Theory and Harmonic Analysis on Semisimple Lie Groups, ISBN 978-0-8218-1526-7, American Mathematical Society .
Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, ISBN 978-0387901909, Springer-Verlag .
Sharpe, Richard W. (1997), Differential Geometry: Cartan's Generalization of Klein's Erlangen Program, ISBN 978-0-387-94732-7, Springer .
Simson, Daniel; Skowronski, Andrzej; Assem, Ibrahim (2007), Elements of the Representation Theory of Associative Algebras, ISBN 978-0-521-88218-7, Cambridge University Press .
Sternberg, Shlomo (1994), Group Theory and Physics, ISBN 978-0-521-55885-3, Cambridge University Press .
Tung, Wu-Ki (1985). Group Theory in Physics 1st ed. New Jersey·London·Singapore·Hong Kong: World Scientific. ISBN 978-9971966577
Weyl, Hermann (1928), Gruppentheorie und Quantenmechanik, ISBN 978-0-486-60269-1 The Theory of Groups and Quantum Mechanics, translated H.P. Robertson, 1931 ed. , S. Hirzel, Leipzig (reprinted 1950, Dover) .
Weyl, Hermann (1946), The Classical Groups: Their Invariants and Representations, ISBN 978-0-691-05756-9 2nd ed. , Princeton University Press (reprinted 1997) .
Wigner, Eugene P. (1939), «On unitary representations of the inhomogeneous Lorentz group», Annals of Mathematics, 40 (1): 149–204, JSTOR 1968551, doi:10.2307/1968551 .

[1] Textos clássicos sobre teoria da representação incluem Curtis & Reiner (1962) e Serre (1977). Outras fontes excelentes são Fulton & Harris (1991) e Goodman & Wallach (1998).

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