Lie algebra extension (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Lie algebra extension" in English language version.

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Otto Schreier (1901 - 1929) was a pioneer in the theory of extension of groups. Along with his rich research papers, his lecture notes were posthumously published (edited by Emanuel Sperner) under the name Einführung in die analytische Geometrie und Algebra (Vol I 1931, Vol II 1935), later in 1951 translated to English in Introduction to Modern Algebra and Matrix Theory. See MacTutor 2015 for further reference. MacTutor (2015). "Schreier biography". MacTutor History of Mathematics. Retrieved 2015-03-08.

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Moody 1967 Moody, R. V. (1967). "Lie algebras associated with generalized Cartan matrices". Bull. Amer. Math. Soc. 73 (2): 217–221. doi:10.1090/S0002-9904-1967-11688-4. MR 0207783. Zbl 0154.27303. (open access)
Zwiebach 2004, Chapter 12 Zwiebach, B. (2004). A First Course in String Theory. Cambridge University Press. ISBN 0-521-83143-1. MR 2069234.
Zwiebach 2004, pp. 219–228 Zwiebach, B. (2004). A First Course in String Theory. Cambridge University Press. ISBN 0-521-83143-1. MR 2069234.
Zwiebach 2004, p. 227 Zwiebach, B. (2004). A First Course in String Theory. Cambridge University Press. ISBN 0-521-83143-1. MR 2069234.
Zwiebach 2004 Equation 6.53 (supported by 6.49, 6.50). Zwiebach, B. (2004). A First Course in String Theory. Cambridge University Press. ISBN 0-521-83143-1. MR 2069234.

ams.org

Dolan 1995 The Beacon of Kac–Moody Symmetry for Physics. (free access) Dolan, L. (1995). "The Beacon of Kac–Moody Symmetry for Physics". Notices of the AMS. 42 (12): 1489–1495. arXiv:hep-th/9601117. Bibcode:1996hep.th....1117D. ISSN 0002-9920.

archive.org (Global: 6^th place; English: 6^th place)

There are alternative routes to quantization, e.g. one postulates the existence of creation and annihilation operators for all particle types with certain exchange symmetries based on which statistics, Bose–Einstein or Fermi–Dirac, the particles obey, in which case the above are derived for scalar bosonic fields using mostly Lorentz invariance and the demand for the unitarity of the S-matrix. In fact, all operators on Hilbert space can be built out of creation and annihilation operators. See e.g. Weinberg (2002), chapters 2–5. Weinberg, S. (2002). The Quantum Theory of Fields. Vol. I. Cambridge University Press. ISBN 978-0-521-55001-7.
Humphreys 1972 Humphreys, J. E. (1972). Introduction to Lie Algebras and Representation Theory (3rd ed.). Berlin·Heidelberg·New York: Springer-Verlag. ISBN 978-3-540-90053-5.
Weinberg 1996, Appendix A, Ch 15. Weinberg, S. (1996). The Quantum Theory of Fields. Vol. II. Cambridge University Press. ISBN 978-0-521-55002-4.
Greiner & Reinhardt 1996 Greiner, W.; Reinhardt, J. (1996). Field Quantization. Springer Publishing. ISBN 978-3-540-59179-5.

arxiv.org (Global: 69^th place; English: 59^th place)

Dolan 1995 The Beacon of Kac–Moody Symmetry for Physics. (free access) Dolan, L. (1995). "The Beacon of Kac–Moody Symmetry for Physics". Notices of the AMS. 42 (12): 1489–1495. arXiv:hep-th/9601117. Bibcode:1996hep.th....1117D. ISSN 0002-9920.

doi.org (Global: 2^nd place; English: 2^nd place)

Miguel Angel Virasoro, born 1940 is an Argentine physicist. The Virasoro algebra, named after him, was first published in Virasoro (1970) Virasoro, M. A. (1970). "Subsidiary conditions and ghosts in dual-resonance models". Phys. Rev. D. 1 (10): 2933–2936. Bibcode:1970PhRvD...1.2933V. doi:10.1103/PhysRevD.1.2933.
Kerf, E.A. De; Bäuerle, G.G.A.; Ten Kroode, A.P.E., eds. (1997). "Extensions of Lie algebras". Lie Algebras - Finite and Infinite Dimensional Lie Algebras and Applications in Physics. Studies in Mathematical Physics. Vol. 7. pp. 5–48. doi:10.1016/S0925-8582(97)80002-4. ISBN 978-0-444-82836-1. The reference states the fact and that it is difficult to show. No further references are given. Expressions on a slightly different form can be found though in Tuynman & Wiegerinck (1987) and Bargmann (1954). Tuynman, G.M.; Wiegerinck, W.A.J.J. (1987). "Central extensions and physics". Journal of Geometry and Physics. 4 (2): 207–258. Bibcode:1987JGP.....4..207T. doi:10.1016/0393-0440(87)90027-1. Bargmann, V. (1954). "On unitary ray representations of continuous groups". Ann. of Math. 59 (1): 1–46. doi:10.2307/1969831. JSTOR 1969831.
Schreier 1926 Schreier, O. (1926). "Uber die Erweiterung von Gruppen I" [On the theory of group extensions I]. Monatshefte für Mathematik (in German). 34 (1): 165–180. doi:10.1007/BF01694897. hdl:10338.dmlcz/127714. S2CID 124731047.
Schreier 1925 Schreier, O. (1925). "Uber die Erweiterung von Gruppen II" [On the theory of group extensions II]. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (in German). 4 (1): 321–346. doi:10.1007/BF02950735. hdl:10338.dmlcz/140420. S2CID 122947636.
Moody 1967 Moody, R. V. (1967). "Lie algebras associated with generalized Cartan matrices". Bull. Amer. Math. Soc. 73 (2): 217–221. doi:10.1090/S0002-9904-1967-11688-4. MR 0207783. Zbl 0154.27303. (open access)
Kerf, E.A. De; Bäuerle, G.G.A.; Ten Kroode, A.P.E., eds. (1997). "Explicit construction of affine Kac-Moody algebras". Lie Algebras - Finite and Infinite Dimensional Lie Algebras and Applications in Physics. Studies in Mathematical Physics. Vol. 7. pp. 49–70. doi:10.1016/S0925-8582(97)80003-6. ISBN 978-0-444-82836-1.
Kerf, E.A. De; Bäuerle, G.G.A.; Ten Kroode, A.P.E., eds. (1997). "Extensions of Lie algebras". Lie Algebras - Finite and Infinite Dimensional Lie Algebras and Applications in Physics. Studies in Mathematical Physics. Vol. 7. pp. 5–48. doi:10.1016/S0925-8582(97)80002-4. ISBN 978-0-444-82836-1.
Bargmann 1954 Bargmann, V. (1954). "On unitary ray representations of continuous groups". Ann. of Math. 59 (1): 1–46. doi:10.2307/1969831. JSTOR 1969831.
Tuynman & Wiegerinck 1987 Tuynman, G.M.; Wiegerinck, W.A.J.J. (1987). "Central extensions and physics". Journal of Geometry and Physics. 4 (2): 207–258. Bibcode:1987JGP.....4..207T. doi:10.1016/0393-0440(87)90027-1.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Schreier 1926 Schreier, O. (1926). "Uber die Erweiterung von Gruppen I" [On the theory of group extensions I]. Monatshefte für Mathematik (in German). 34 (1): 165–180. doi:10.1007/BF01694897. hdl:10338.dmlcz/127714. S2CID 124731047.
Schreier 1925 Schreier, O. (1925). "Uber die Erweiterung von Gruppen II" [On the theory of group extensions II]. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (in German). 4 (1): 321–346. doi:10.1007/BF02950735. hdl:10338.dmlcz/140420. S2CID 122947636.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Miguel Angel Virasoro, born 1940 is an Argentine physicist. The Virasoro algebra, named after him, was first published in Virasoro (1970) Virasoro, M. A. (1970). "Subsidiary conditions and ghosts in dual-resonance models". Phys. Rev. D. 1 (10): 2933–2936. Bibcode:1970PhRvD...1.2933V. doi:10.1103/PhysRevD.1.2933.
Kerf, E.A. De; Bäuerle, G.G.A.; Ten Kroode, A.P.E., eds. (1997). "Extensions of Lie algebras". Lie Algebras - Finite and Infinite Dimensional Lie Algebras and Applications in Physics. Studies in Mathematical Physics. Vol. 7. pp. 5–48. doi:10.1016/S0925-8582(97)80002-4. ISBN 978-0-444-82836-1. The reference states the fact and that it is difficult to show. No further references are given. Expressions on a slightly different form can be found though in Tuynman & Wiegerinck (1987) and Bargmann (1954). Tuynman, G.M.; Wiegerinck, W.A.J.J. (1987). "Central extensions and physics". Journal of Geometry and Physics. 4 (2): 207–258. Bibcode:1987JGP.....4..207T. doi:10.1016/0393-0440(87)90027-1. Bargmann, V. (1954). "On unitary ray representations of continuous groups". Ann. of Math. 59 (1): 1–46. doi:10.2307/1969831. JSTOR 1969831.
Dolan 1995 The Beacon of Kac–Moody Symmetry for Physics. (free access) Dolan, L. (1995). "The Beacon of Kac–Moody Symmetry for Physics". Notices of the AMS. 42 (12): 1489–1495. arXiv:hep-th/9601117. Bibcode:1996hep.th....1117D. ISSN 0002-9920.
Tuynman & Wiegerinck 1987 Tuynman, G.M.; Wiegerinck, W.A.J.J. (1987). "Central extensions and physics". Journal of Geometry and Physics. 4 (2): 207–258. Bibcode:1987JGP.....4..207T. doi:10.1016/0393-0440(87)90027-1.

jstor.org (Global: 26^th place; English: 20^th place)

Kerf, E.A. De; Bäuerle, G.G.A.; Ten Kroode, A.P.E., eds. (1997). "Extensions of Lie algebras". Lie Algebras - Finite and Infinite Dimensional Lie Algebras and Applications in Physics. Studies in Mathematical Physics. Vol. 7. pp. 5–48. doi:10.1016/S0925-8582(97)80002-4. ISBN 978-0-444-82836-1. The reference states the fact and that it is difficult to show. No further references are given. Expressions on a slightly different form can be found though in Tuynman & Wiegerinck (1987) and Bargmann (1954). Tuynman, G.M.; Wiegerinck, W.A.J.J. (1987). "Central extensions and physics". Journal of Geometry and Physics. 4 (2): 207–258. Bibcode:1987JGP.....4..207T. doi:10.1016/0393-0440(87)90027-1. Bargmann, V. (1954). "On unitary ray representations of continuous groups". Ann. of Math. 59 (1): 1–46. doi:10.2307/1969831. JSTOR 1969831.
Bargmann 1954 Bargmann, V. (1954). "On unitary ray representations of continuous groups". Ann. of Math. 59 (1): 1–46. doi:10.2307/1969831. JSTOR 1969831.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Schreier 1926 Schreier, O. (1926). "Uber die Erweiterung von Gruppen I" [On the theory of group extensions I]. Monatshefte für Mathematik (in German). 34 (1): 165–180. doi:10.1007/BF01694897. hdl:10338.dmlcz/127714. S2CID 124731047.
Schreier 1925 Schreier, O. (1925). "Uber die Erweiterung von Gruppen II" [On the theory of group extensions II]. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (in German). 4 (1): 321–346. doi:10.1007/BF02950735. hdl:10338.dmlcz/140420. S2CID 122947636.

st-and.ac.uk (Global: 3,503^rd place; English: 3,612^th place)

www-history.mcs.st-and.ac.uk

Otto Schreier (1901 - 1929) was a pioneer in the theory of extension of groups. Along with his rich research papers, his lecture notes were posthumously published (edited by Emanuel Sperner) under the name Einführung in die analytische Geometrie und Algebra (Vol I 1931, Vol II 1935), later in 1951 translated to English in Introduction to Modern Algebra and Matrix Theory. See MacTutor 2015 for further reference. MacTutor (2015). "Schreier biography". MacTutor History of Mathematics. Retrieved 2015-03-08.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Dolan 1995 The Beacon of Kac–Moody Symmetry for Physics. (free access) Dolan, L. (1995). "The Beacon of Kac–Moody Symmetry for Physics". Notices of the AMS. 42 (12): 1489–1495. arXiv:hep-th/9601117. Bibcode:1996hep.th....1117D. ISSN 0002-9920.

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Moody 1967 Moody, R. V. (1967). "Lie algebras associated with generalized Cartan matrices". Bull. Amer. Math. Soc. 73 (2): 217–221. doi:10.1090/S0002-9904-1967-11688-4. MR 0207783. Zbl 0154.27303. (open access)

Lie algebra extension (English Wikipedia)

amazon.com (Global: 105th place; English: 79th place)

ams.org (Global: 451st place; English: 277th place)

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ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 69th place; English: 59th place)

doi.org (Global: 2nd place; English: 2nd place)

handle.net (Global: 102nd place; English: 76th place)