Virasoro algebra (English Wikipedia)

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

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P. Goddard, A. Kent & D. Olive (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. MR 0826859. S2CID 91181508. Zbl 0588.17014.

arxiv.org

A. Kent (1991). "Singular vectors of the Virasoro algebra". Physics Letters B. 273 (1–2): 56–62. arXiv:hep-th/9204097. Bibcode:1991PhLB..273...56K. doi:10.1016/0370-2693(91)90553-3. S2CID 15105921.
Watts, Gérard M T (2025). "Explicit expressions for Virasoro singular vectors". Journal of High Energy Physics. 2025 (4): 131. arXiv:2412.07505. Bibcode:2025JHEP...04..131W. doi:10.1007/JHEP04(2025)131.
Fortin, Jean-François; Quintavalle, Lorenzo; Skiba, Witold (2025). "The Virasoro Completeness Relation and Inverse Shapovalov Form". Physical Review D. 111 (8): 085010. arXiv:2409.12224. Bibcode:2025PhRvD.111h5010F. doi:10.1103/PhysRevD.111.085010.
Rabin, J. M. (1995). "Super elliptic curves". Journal of Geometry and Physics. 15 (3): 252–280. arXiv:hep-th/9302105. Bibcode:1995JGP....15..252R. doi:10.1016/0393-0440(94)00012-S. S2CID 10921054.

cern.ch

cds.cern.ch

R. C. Brower; C. B. Thorn (1971). "Eliminating spurious states from the dual resonance model". Nuclear Physics B. 31 (1): 163–182. Bibcode:1971NuPhB..31..163B. doi:10.1016/0550-3213(71)90452-4.

doi.org

A Mathematical Introduction to Conformal Field Theory. Lecture Notes in Physics. Vol. 759. 2008. doi:10.1007/978-3-540-68628-6. ISBN 978-3-540-68625-5. ISSN 0075-8450.
Fairlie, D. B.; Nuyts, J.; Zachos, C. K. (1988). "A presentation for the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 117 (4): 595. Bibcode:1988CMaPh.117..595F. doi:10.1007/BF01218387. S2CID 119811901.
Uretsky, J. L. (1989). "Redundancy of conditions for a Virasoro algebra". Communications in Mathematical Physics. 122 (1): 171–173. Bibcode:1989CMaPh.122..171U. doi:10.1007/BF01221412. S2CID 119887710.
A. Kent (1991). "Singular vectors of the Virasoro algebra". Physics Letters B. 273 (1–2): 56–62. arXiv:hep-th/9204097. Bibcode:1991PhLB..273...56K. doi:10.1016/0370-2693(91)90553-3. S2CID 15105921.
Watts, Gérard M T (2025). "Explicit expressions for Virasoro singular vectors". Journal of High Energy Physics. 2025 (4): 131. arXiv:2412.07505. Bibcode:2025JHEP...04..131W. doi:10.1007/JHEP04(2025)131.
Fortin, Jean-François; Quintavalle, Lorenzo; Skiba, Witold (2025). "The Virasoro Completeness Relation and Inverse Shapovalov Form". Physical Review D. 111 (8): 085010. arXiv:2409.12224. Bibcode:2025PhRvD.111h5010F. doi:10.1103/PhysRevD.111.085010.
Feigin, B. L.; Fuchs, D. B. (1984). "Verma modules over the virasoro algebra". Topology. Vol. 1060. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 230–245. doi:10.1007/bfb0099939. ISBN 978-3-540-13337-7.
Friedan, D., Qiu, Z. and Shenker, S. (1984). "Conformal invariance, unitarity and critical exponents in two dimensions". Physical Review Letters. 52 (18): 1575–1578. Bibcode:1984PhRvL..52.1575F. doi:10.1103/PhysRevLett.52.1575. S2CID 122320349.{{cite journal}}: CS1 maint: multiple names: authors list (link)
P. Goddard, A. Kent & D. Olive (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. MR 0826859. S2CID 91181508. Zbl 0588.17014.
Krichever, I. M.; Novikov, S.P. (1987). "Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons". Funkts. Anal. Appl. 21 (2): 46–63. doi:10.1007/BF01078026. S2CID 55989582.
Rabin, J. M. (1995). "Super elliptic curves". Journal of Geometry and Physics. 15 (3): 252–280. arXiv:hep-th/9302105. Bibcode:1995JGP....15..252R. doi:10.1016/0393-0440(94)00012-S. S2CID 10921054.
E. Cartan (1909). "Les groupes de transformations continus, infinis, simples". Annales Scientifiques de l'École Normale Supérieure. 26: 93–161. doi:10.24033/asens.603. JFM 40.0193.02.
R. E. Block (1966). "On the Mills–Seligman axioms for Lie algebras of classical type". Transactions of the American Mathematical Society. 121 (2): 378–392. doi:10.1090/S0002-9947-1966-0188356-3. JSTOR 1994485.
Gel'fand, I. M.; Fuks, D. B. (1969). "The cohomologies of the lie algebra of the vector fields in a circle". Functional Analysis and Its Applications. 2 (4): 342–343. doi:10.1007/BF01075687. ISSN 0016-2663.
Virasoro, M. A. (1970-05-15). "Subsidiary Conditions and Ghosts in Dual-Resonance Models". Physical Review D. 1 (10): 2933–2936. Bibcode:1970PhRvD...1.2933V. doi:10.1103/PhysRevD.1.2933. ISSN 0556-2821.
R. C. Brower; C. B. Thorn (1971). "Eliminating spurious states from the dual resonance model". Nuclear Physics B. 31 (1): 163–182. Bibcode:1971NuPhB..31..163B. doi:10.1016/0550-3213(71)90452-4.

harvard.edu

ui.adsabs.harvard.edu

Fairlie, D. B.; Nuyts, J.; Zachos, C. K. (1988). "A presentation for the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 117 (4): 595. Bibcode:1988CMaPh.117..595F. doi:10.1007/BF01218387. S2CID 119811901.
Uretsky, J. L. (1989). "Redundancy of conditions for a Virasoro algebra". Communications in Mathematical Physics. 122 (1): 171–173. Bibcode:1989CMaPh.122..171U. doi:10.1007/BF01221412. S2CID 119887710.
A. Kent (1991). "Singular vectors of the Virasoro algebra". Physics Letters B. 273 (1–2): 56–62. arXiv:hep-th/9204097. Bibcode:1991PhLB..273...56K. doi:10.1016/0370-2693(91)90553-3. S2CID 15105921.
Watts, Gérard M T (2025). "Explicit expressions for Virasoro singular vectors". Journal of High Energy Physics. 2025 (4): 131. arXiv:2412.07505. Bibcode:2025JHEP...04..131W. doi:10.1007/JHEP04(2025)131.
Fortin, Jean-François; Quintavalle, Lorenzo; Skiba, Witold (2025). "The Virasoro Completeness Relation and Inverse Shapovalov Form". Physical Review D. 111 (8): 085010. arXiv:2409.12224. Bibcode:2025PhRvD.111h5010F. doi:10.1103/PhysRevD.111.085010.
Friedan, D., Qiu, Z. and Shenker, S. (1984). "Conformal invariance, unitarity and critical exponents in two dimensions". Physical Review Letters. 52 (18): 1575–1578. Bibcode:1984PhRvL..52.1575F. doi:10.1103/PhysRevLett.52.1575. S2CID 122320349.{{cite journal}}: CS1 maint: multiple names: authors list (link)
P. Goddard, A. Kent & D. Olive (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. MR 0826859. S2CID 91181508. Zbl 0588.17014.
Rabin, J. M. (1995). "Super elliptic curves". Journal of Geometry and Physics. 15 (3): 252–280. arXiv:hep-th/9302105. Bibcode:1995JGP....15..252R. doi:10.1016/0393-0440(94)00012-S. S2CID 10921054.
Virasoro, M. A. (1970-05-15). "Subsidiary Conditions and Ghosts in Dual-Resonance Models". Physical Review D. 1 (10): 2933–2936. Bibcode:1970PhRvD...1.2933V. doi:10.1103/PhysRevD.1.2933. ISSN 0556-2821.
R. C. Brower; C. B. Thorn (1971). "Eliminating spurious states from the dual resonance model". Nuclear Physics B. 31 (1): 163–182. Bibcode:1971NuPhB..31..163B. doi:10.1016/0550-3213(71)90452-4.

jstor.org

R. E. Block (1966). "On the Mills–Seligman axioms for Lie algebras of classical type". Transactions of the American Mathematical Society. 121 (2): 378–392. doi:10.1090/S0002-9947-1966-0188356-3. JSTOR 1994485.

projecteuclid.org

Fairlie, D. B.; Nuyts, J.; Zachos, C. K. (1988). "A presentation for the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 117 (4): 595. Bibcode:1988CMaPh.117..595F. doi:10.1007/BF01218387. S2CID 119811901.
P. Goddard, A. Kent & D. Olive (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. MR 0826859. S2CID 91181508. Zbl 0588.17014.

semanticscholar.org

api.semanticscholar.org

Fairlie, D. B.; Nuyts, J.; Zachos, C. K. (1988). "A presentation for the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 117 (4): 595. Bibcode:1988CMaPh.117..595F. doi:10.1007/BF01218387. S2CID 119811901.
Uretsky, J. L. (1989). "Redundancy of conditions for a Virasoro algebra". Communications in Mathematical Physics. 122 (1): 171–173. Bibcode:1989CMaPh.122..171U. doi:10.1007/BF01221412. S2CID 119887710.
A. Kent (1991). "Singular vectors of the Virasoro algebra". Physics Letters B. 273 (1–2): 56–62. arXiv:hep-th/9204097. Bibcode:1991PhLB..273...56K. doi:10.1016/0370-2693(91)90553-3. S2CID 15105921.
Friedan, D., Qiu, Z. and Shenker, S. (1984). "Conformal invariance, unitarity and critical exponents in two dimensions". Physical Review Letters. 52 (18): 1575–1578. Bibcode:1984PhRvL..52.1575F. doi:10.1103/PhysRevLett.52.1575. S2CID 122320349.{{cite journal}}: CS1 maint: multiple names: authors list (link)
P. Goddard, A. Kent & D. Olive (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. MR 0826859. S2CID 91181508. Zbl 0588.17014.
Krichever, I. M.; Novikov, S.P. (1987). "Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons". Funkts. Anal. Appl. 21 (2): 46–63. doi:10.1007/BF01078026. S2CID 55989582.
Rabin, J. M. (1995). "Super elliptic curves". Journal of Geometry and Physics. 15 (3): 252–280. arXiv:hep-th/9302105. Bibcode:1995JGP....15..252R. doi:10.1016/0393-0440(94)00012-S. S2CID 10921054.

springer.com

link.springer.com

A Mathematical Introduction to Conformal Field Theory. Lecture Notes in Physics. Vol. 759. 2008. doi:10.1007/978-3-540-68628-6. ISBN 978-3-540-68625-5. ISSN 0075-8450.

worldcat.org

search.worldcat.org

A Mathematical Introduction to Conformal Field Theory. Lecture Notes in Physics. Vol. 759. 2008. doi:10.1007/978-3-540-68628-6. ISBN 978-3-540-68625-5. ISSN 0075-8450.
Gel'fand, I. M.; Fuks, D. B. (1969). "The cohomologies of the lie algebra of the vector fields in a circle". Functional Analysis and Its Applications. 2 (4): 342–343. doi:10.1007/BF01075687. ISSN 0016-2663.
Virasoro, M. A. (1970-05-15). "Subsidiary Conditions and Ghosts in Dual-Resonance Models". Physical Review D. 1 (10): 2933–2936. Bibcode:1970PhRvD...1.2933V. doi:10.1103/PhysRevD.1.2933. ISSN 0556-2821.

zbmath.org

P. Goddard, A. Kent & D. Olive (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Communications in Mathematical Physics. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. MR 0826859. S2CID 91181508. Zbl 0588.17014.
E. Cartan (1909). "Les groupes de transformations continus, infinis, simples". Annales Scientifiques de l'École Normale Supérieure. 26: 93–161. doi:10.24033/asens.603. JFM 40.0193.02.