Group cohomology (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Group cohomology" in English language version.

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Page 62 of Milne 2008 or section VII.3 of Serre 1979 Milne, James (2013), "Chapter II: The Cohomology of Groups", Class Field Theory, vol. v4.02 Serre, Jean-Pierre (1979). "Chapter VII". Local fields. Graduate Texts in Mathematics. Vol. 67. Berlin, New York: Springer-Verlag. ISBN 978-0-387-90424-5. MR 0554237. Zbl 0423.12016.
Huang, Hua-Lin; Liu, Gongxiang; Ye, Yu (2014). "The braided monoidal structures on a class of linear Gr-categories". Algebras and Representation Theory. 17 (4): 1249–1265. arXiv:1206.5402. doi:10.1007/s10468-013-9445-8. MR 3228486. See Proposition 2.3.
(Brown 1972), §III.9 Brown, Kenneth S. (1972), Cohomology of Groups, Graduate Texts in Mathematics, vol. 87, Springer Verlag, ISBN 978-0-387-90688-1, MR 0672956
(Brown 1972), Exercise III.1.3 Brown, Kenneth S. (1972), Cohomology of Groups, Graduate Texts in Mathematics, vol. 87, Springer Verlag, ISBN 978-0-387-90688-1, MR 0672956
(Adem & Milgram 2004), Chapter II. Adem, Alejandro; Milgram, R. James (2004), Cohomology of Finite Groups, Grundlehren der Mathematischen Wissenschaften, vol. 309 (2nd ed.), Springer-Verlag, doi:10.1007/978-3-662-06280-7, ISBN 978-3-540-20283-7, MR 2035696, Zbl 1061.20044
(Brown 1972), §VI.9 Brown, Kenneth S. (1972), Cohomology of Groups, Graduate Texts in Mathematics, vol. 87, Springer Verlag, ISBN 978-0-387-90688-1, MR 0672956

arxiv.org

Huang, Hua-Lin; Liu, Gongxiang; Ye, Yu (2014). "The braided monoidal structures on a class of linear Gr-categories". Algebras and Representation Theory. 17 (4): 1249–1265. arXiv:1206.5402. doi:10.1007/s10468-013-9445-8. MR 3228486. See Proposition 2.3.
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang (22 January 2015). "Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond". Physical Review Letters. 114 (3): 031601. arXiv:1405.7689. Bibcode:2015PhRvL.114c1601W. doi:10.1103/physrevlett.114.031601. ISSN 0031-9007. PMID 25658993. S2CID 2370407.
Wen, Xiao-Gang (4 May 2015). "Construction of bosonic symmetry-protected-trivial states and their topological invariants via G×SO(∞) nonlinear σ models". Physical Review B. 91 (20): 205101. arXiv:1410.8477. Bibcode:2015PhRvB..91t5101W. doi:10.1103/physrevb.91.205101. ISSN 1098-0121. S2CID 13950401.

doi.org

Huang, Hua-Lin; Liu, Gongxiang; Ye, Yu (2014). "The braided monoidal structures on a class of linear Gr-categories". Algebras and Representation Theory. 17 (4): 1249–1265. arXiv:1206.5402. doi:10.1007/s10468-013-9445-8. MR 3228486. See Proposition 2.3.
Stasheff, James D. (1978-07-01). "Continuous cohomology of groups and classifying spaces". Bulletin of the American Mathematical Society. 84 (4): 513–531. doi:10.1090/s0002-9904-1978-14488-7. ISSN 0002-9904.
(Adem & Milgram 2004), Chapter II. Adem, Alejandro; Milgram, R. James (2004), Cohomology of Finite Groups, Grundlehren der Mathematischen Wissenschaften, vol. 309 (2nd ed.), Springer-Verlag, doi:10.1007/978-3-662-06280-7, ISBN 978-3-540-20283-7, MR 2035696, Zbl 1061.20044
In this case, the coefficients are rational. Borel, Armand (1974). "Stable real cohomology of arithmetic groups". Annales Scientifiques de l'École Normale Supérieure. Série 4. 7 (2): 235–272. doi:10.24033/asens.1269.
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang (22 January 2015). "Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond". Physical Review Letters. 114 (3): 031601. arXiv:1405.7689. Bibcode:2015PhRvL.114c1601W. doi:10.1103/physrevlett.114.031601. ISSN 0031-9007. PMID 25658993. S2CID 2370407.
Wen, Xiao-Gang (4 May 2015). "Construction of bosonic symmetry-protected-trivial states and their topological invariants via G×SO(∞) nonlinear σ models". Physical Review B. 91 (20): 205101. arXiv:1410.8477. Bibcode:2015PhRvB..91t5101W. doi:10.1103/physrevb.91.205101. ISSN 1098-0121. S2CID 13950401.

harvard.edu

ui.adsabs.harvard.edu

Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang (22 January 2015). "Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond". Physical Review Letters. 114 (3): 031601. arXiv:1405.7689. Bibcode:2015PhRvL.114c1601W. doi:10.1103/physrevlett.114.031601. ISSN 0031-9007. PMID 25658993. S2CID 2370407.
Wen, Xiao-Gang (4 May 2015). "Construction of bosonic symmetry-protected-trivial states and their topological invariants via G×SO(∞) nonlinear σ models". Physical Review B. 91 (20): 205101. arXiv:1410.8477. Bibcode:2015PhRvB..91t5101W. doi:10.1103/physrevb.91.205101. ISSN 1098-0121. S2CID 13950401.

jmilne.org

Page 62 of Milne 2008 or section VII.3 of Serre 1979 Milne, James (2013), "Chapter II: The Cohomology of Groups", Class Field Theory, vol. v4.02 Serre, Jean-Pierre (1979). "Chapter VII". Local fields. Graduate Texts in Mathematics. Vol. 67. Berlin, New York: Springer-Verlag. ISBN 978-0-387-90424-5. MR 0554237. Zbl 0423.12016.
Remark II.1.21 of Milne 2008 Milne, James (2013), "Chapter II: The Cohomology of Groups", Class Field Theory, vol. v4.02

nih.gov

pubmed.ncbi.nlm.nih.gov

Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang (22 January 2015). "Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond". Physical Review Letters. 114 (3): 031601. arXiv:1405.7689. Bibcode:2015PhRvL.114c1601W. doi:10.1103/physrevlett.114.031601. ISSN 0031-9007. PMID 25658993. S2CID 2370407.

semanticscholar.org

api.semanticscholar.org

Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang (22 January 2015). "Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond". Physical Review Letters. 114 (3): 031601. arXiv:1405.7689. Bibcode:2015PhRvL.114c1601W. doi:10.1103/physrevlett.114.031601. ISSN 0031-9007. PMID 25658993. S2CID 2370407.
Wen, Xiao-Gang (4 May 2015). "Construction of bosonic symmetry-protected-trivial states and their topological invariants via G×SO(∞) nonlinear σ models". Physical Review B. 91 (20): 205101. arXiv:1410.8477. Bibcode:2015PhRvB..91t5101W. doi:10.1103/physrevb.91.205101. ISSN 1098-0121. S2CID 13950401.

umn.edu

www-users.math.umn.edu

Webb, Peter. "An Introduction to the Cohomology of Groups" (PDF). Archived (PDF) from the original on 6 May 2020.

web.archive.org

Webb, Peter. "An Introduction to the Cohomology of Groups" (PDF). Archived (PDF) from the original on 6 May 2020.

worldcat.org

search.worldcat.org

Dummit, David Steven; Foote, Richard M. (14 July 2003). Abstract algebra (Third ed.). Hoboken, NJ: John Wiley & Sons. p. 801. ISBN 0-471-43334-9. OCLC 52559229.
Brown, Kenneth S. (6 December 2012). Cohomology of groups. Graduate Texts in Mathematics. Vol. 87. New York, New York: Springer. p. 35. ISBN 978-1-4684-9327-6. OCLC 853269200.
Evens, Leonard. (1991). The cohomology of groups. Oxford: Clarendon Press. ISBN 0-19-853580-5. OCLC 23732584.
Hatcher, Allen (2002). Algebraic topology. Cambridge: Cambridge University Press. p. 43. ISBN 0-521-79160-X. OCLC 45420394.
Stasheff, James D. (1978-07-01). "Continuous cohomology of groups and classifying spaces". Bulletin of the American Mathematical Society. 84 (4): 513–531. doi:10.1090/s0002-9904-1978-14488-7. ISSN 0002-9904.
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang (22 January 2015). "Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond". Physical Review Letters. 114 (3): 031601. arXiv:1405.7689. Bibcode:2015PhRvL.114c1601W. doi:10.1103/physrevlett.114.031601. ISSN 0031-9007. PMID 25658993. S2CID 2370407.
Wen, Xiao-Gang (4 May 2015). "Construction of bosonic symmetry-protected-trivial states and their topological invariants via G×SO(∞) nonlinear σ models". Physical Review B. 91 (20): 205101. arXiv:1410.8477. Bibcode:2015PhRvB..91t5101W. doi:10.1103/physrevb.91.205101. ISSN 1098-0121. S2CID 13950401.

worldcat.org

Evens, Leonard. (1991). The cohomology of groups. Oxford: Clarendon Press. ISBN 0-19-853580-5. OCLC 23732584.

zbmath.org

For example, the two are isomorphic if all primes p such that G has p-torsion are invertible in k. See (Knudson 2001), Theorem A.1.19 for the precise statement. Knudson, Kevin P. (2001), Homology of Linear Groups, Progress in Mathematics, vol. 193, Birkhäuser Verlag, Zbl 0997.20045
Page 62 of Milne 2008 or section VII.3 of Serre 1979 Milne, James (2013), "Chapter II: The Cohomology of Groups", Class Field Theory, vol. v4.02 Serre, Jean-Pierre (1979). "Chapter VII". Local fields. Graduate Texts in Mathematics. Vol. 67. Berlin, New York: Springer-Verlag. ISBN 978-0-387-90424-5. MR 0554237. Zbl 0423.12016.
(Knudson 2001), Chapter 4 Knudson, Kevin P. (2001), Homology of Linear Groups, Progress in Mathematics, vol. 193, Birkhäuser Verlag, Zbl 0997.20045
(Adem & Milgram 2004), Chapter II. Adem, Alejandro; Milgram, R. James (2004), Cohomology of Finite Groups, Grundlehren der Mathematischen Wissenschaften, vol. 309 (2nd ed.), Springer-Verlag, doi:10.1007/978-3-662-06280-7, ISBN 978-3-540-20283-7, MR 2035696, Zbl 1061.20044