Homology of integral upper-triangular matrices
HTML articles powered by AMS MathViewer
- by W. G. Dwyer PDF
- Proc. Amer. Math. Soc. 94 (1985), 523-528 Request permission
Abstract:
We calculate the homology of the multiplicative group of integral upper-triangular $n \times n$ matrices at all primes $p \geqslant n - 1$.References
- F. Bachmann and L. Grünenfelder, Über Lie-Ringe von Gruppen und ihre universellen Enveloppen, Comment. Math. Helv. 47 (1972), 332–340 (German). MR 318248, DOI 10.1007/BF02566808
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- Roger W. Carter and George Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 193–242. MR 354887, DOI 10.1007/BF01214125
- Howard Garland and James Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), no. 1, 37–76. MR 414645, DOI 10.1007/BF01418970
- Luzius Grünenfelder, On the homology of filtered and graded rings, J. Pure Appl. Algebra 14 (1979), no. 1, 21–37. MR 515484, DOI 10.1016/0022-4049(79)90010-0
- Bertram Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. (2) 74 (1961), 329–387. MR 142696, DOI 10.2307/1970237
- Larry A. Lambe and Stewart B. Priddy, Cohomology of nilmanifolds and torsion-free, nilpotent groups, Trans. Amer. Math. Soc. 273 (1982), no. 1, 39–55. MR 664028, DOI 10.1090/S0002-9947-1982-0664028-2
- Katsumi Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. (2) 59 (1954), 531–538. MR 64057, DOI 10.2307/1969716
- Daniel Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 (1971), 29–56 (1971). MR 290382, DOI 10.1016/0001-8708(71)90041-7 J. P. Serre, Algèbre locale multiplicités, Lecture Notes in Math., vol. 11, Springer, New York, 1975.
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 523-528
- MSC: Primary 55R35; Secondary 17B56, 20H25, 55S30
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787905-9
- MathSciNet review: 787905