On the theory of Frobenius extensions and its application to Lie superalgebras
HTML articles powered by AMS MathViewer
- by Allen D. Bell and Rolf Farnsteiner
- Trans. Amer. Math. Soc. 335 (1993), 407-424
- DOI: https://doi.org/10.1090/S0002-9947-1993-1097163-5
- PDF | Request permission
Abstract:
By using an approach to the theory of Frobenius extensions that emphasizes notions related to associative forms, we obtain results concerning the trace and corestriction mappings and transitivity. These are employed to show that the extension of enveloping algebras determined by a subalgebra of a Lie superalgebra is a Frobenius extension, and to study certain questions in representation theory.References
- Rolf Farnsteiner, Lie theoretic methods in cohomology theory, Lie algebras, Madison 1987, Lecture Notes in Math., vol. 1373, Springer, Berlin, 1989, pp. 93–110. MR 1007327, DOI 10.1007/BFb0088890
- Rolf Farnsteiner, On the cohomology of ring extensions, Adv. Math. 87 (1991), no. 1, 42–70. MR 1102964, DOI 10.1016/0001-8708(91)90061-B
- Rolf Farnsteiner and Helmut Strade, Shapiro’s lemma and its consequences in the cohomology theory of modular Lie algebras, Math. Z. 206 (1991), no. 1, 153–168. MR 1086821, DOI 10.1007/BF02571333
- Kazuhiko Hirata, On relative homological algebra of Frobenius extensions, Nagoya Math. J. 15 (1959), 17–28. MR 108526
- G. Hochschild, Relative homological algebra, Trans. Amer. Math. Soc. 82 (1956), 246–269. MR 80654, DOI 10.1090/S0002-9947-1956-0080654-0
- G. Hochschild, Semisimplicity of $2$-graded Lie algebras, Illinois J. Math. 20 (1976), no. 1, 107–123. MR 387362
- Nathan Jacobson, Lie algebras, Dover Publications, Inc., New York, 1979. Republication of the 1962 original. MR 559927
- V. G. Kac, Lie superalgebras, Advances in Math. 26 (1977), no. 1, 8–96. MR 486011, DOI 10.1016/0001-8708(77)90017-2 —, Representations of classical Lie superalgebras, Lecture Notes in Math., vol. 676 (K. Bleuler, H. Pertry, and A. Reetz, eds.), Springer-Verlag, Berlin, 1977, pp. 579-626.
- Friedrich Kasch, Projektive Frobenius-Erweiterungen, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1960/61 (1960/1961), 87–109 (German). MR 0132085 —, Dualitätseigenschafter von Frobeniuserweiterungen, Math. Z. 77 (1961), 219-227.
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
- Tadasi Nakayama and Tosiro Tsuzuku, On Frobenius extensions. I, Nagoya Math. J. 17 (1960), 89–110. MR 124375
- Tadasi Nakayama and Tosiro Tsuzuku, On Frobenius extensions. II, Nagoya Math. J. 19 (1961), 127–148. MR 140540
- Bodo Pareigis, Einige Bemerkungen über Frobenius-Erweiterungen, Math. Ann. 153 (1964), 1–13 (German). MR 166222, DOI 10.1007/BF01361702
- Guang Yu Shen, Graded modules of graded Lie algebras of Cartan type. II. Positive and negative graded modules, Sci. Sinica Ser. A 29 (1986), no. 10, 1009–1019. MR 877285
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 335 (1993), 407-424
- MSC: Primary 17B70; Secondary 17A70, 17B55
- DOI: https://doi.org/10.1090/S0002-9947-1993-1097163-5
- MathSciNet review: 1097163