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Communications in Algebra Volume 46, 2018 - Issue 3
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Original Articles

Cohomology of SL2 and related structures

Klaus LuxDepartment of Mathematics, University of Arizona, Tucson, Arizona, USA
,
Nham V. NgoDepartment of Mathematics, University of North Georgia–Gainesville, Oakwood, Georgia, USACorrespondence[email protected]
&
Yichao ZhangDepartment of Mathematics, Harbin Institute of Technology, Harbin, P. R. China
Pages 979-1000 | Received 23 Jan 2017, Published online: 12 Jul 2017

References

  • Baier, S., Lamzin, S., Miemietz, V. (2013). Dimensions of Ext-groups of Weyl modules for GL2, Available at: https://arxiv.org/pdf/1305.5947v3.pdf. Accessed date 11/25/2016.
  • Bendel, C., Nakano, D., Pillen, C. (2007). Second cohomology for Frobenius kernels and related structures. Adv. Math. 209:162–197.
  • Bendel, C., Nakano, D., Pillen, C. (2016). Third cohomology for Frobenius kernels and related structures. Proc. Symp. Pure Math. 92:81–118.
  • Bendel, C., Nakano, N., Parshall, B., Pillen, C., Scott, L., Stewart, D. (2015). Bounding extensions for finite groups and Frobenius kernels. Algebras Represent. Theory 18:739–760.
  • Carlson, J. F. (1983). The cohomology of irreducible modules over SL(2,pn). Proc. London Math. Soc. 47:480–492.
  • Cox, A., Erdmann, K. (2000). On Ext2 between Weyl modules for quantum GLn. Math. Proc. Cambridge Philos. Soc. 128:441–463.
  • Cline, E., Parshall, B., Scott, L. (1980). Cohomology, hyperalgebras, and representations. J. Algebra 63:98–123.
  • Cline, E., Parshall, B., Scott, L., van der Kallen, W. (1977). Rational and generic cohomology. Invent. Math. 39:143–163.
  • Erdmann, K. (1995). Ext1 for Weyl modules for SL2(K). Math. Z. 218:447–459.
  • Erdmann, K., Hannabuss, K. C., Parker, A. (2013). Bounding and unbounding higher extensions for SL2. J. Algebra 389:98–118.
  • Grosswald, E. (1984). Topics from the Theory of Numbers. Boston, Massachusetts: Springer Science & Business Media.
  • Hemmer, D. J. (2009). Cohomology and generic cohomology of Specht modules for the symmetric group. J. Algebra 322:1498–1515.
  • Hemmer, D. J., Nakano, D. K. (2006). On the cohomology of Specht modules. J. Algebra 306:191–200.
  • Jantzen, J. C. (2003). Representations of Algebraic Groups. Mathematical Surveys and Monographs, Vol. 107. Providence, RI: American Mathematical Society.
  • Kleshchev, A. S., Nakano, D. K. (2001). On comparing the cohomology of general linear and symmetric groups. Pacific J. Math. 201:339–355.
  • Miemietz, V., Turner, W. (2013). The Weyl extension algebra of GL2(𝔽¯p). Adv. Math. 246:144–197.
  • Ngo, N. V. (2013). Cohomology for Frobenius kernels of SL2. J. Algebra 396:39–60.
  • Parker, A. E. (2007). Higher extensions between modules for SL2. Adv. Math. 209:381–405.
  • Parshall, B. J., Scott, L. L. (2011). Bounding Ext for modules for algebraic groups, finite groups and quantum groups. Adv. Math. 226:2065–2088.
  • Parshall, B. J., Scott, L. L. (2012). Cohomological growth rates and Kazhdan-Lusztig polynomials. Israel J. Math. 191:85–110.
  • Stewart, D. I. (2012). Unbounding Ext. J. Algebra 365:1–11.

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