An algebraic 𝑆𝐿₂-vector bundle over 𝑅₂ as a variety

Nagase, Teruko

doi:10.1090/S0002-9939-96-03779-3

An algebraic $SL_2$-vector bundle over $R_2$ as a variety
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Proc. Amer. Math. Soc. 124 (1996), 3325-3331 Request permission

Abstract:

We show the stable triviality of all the elements in $\operatorname {VEC}(R_{2},R_{n})$ concretely, and describe $\operatorname {VEC}(R_{2},R_{n})$ as surjection classes from a trivial bundle to another. The results also contain the explicit description of non-linearizable $SL_{2}$ actions on $\mathbb {C}^{n}$.

References

H. Bass and W. Haboush, Linearizing certain reductive group actions, Trans. Amer. Math. Soc. 292 (1985), no. 2, 463–482. MR 808732, DOI 10.1090/S0002-9947-1985-0808732-4
H. Bass and W. Haboush, Some equivariant $K$-theory of affine algebraic group actions, Comm. Algebra 15 (1987), no. 1-2, 181–217. MR 876977, DOI 10.1080/00927878708823417
Friedrich Knop, Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Räumen, Invent. Math. 105 (1991), no. 1, 217–220 (German). MR 1109627, DOI 10.1007/BF01232264
Hanspeter Kraft and Gerald W. Schwarz, Reductive group actions with one-dimensional quotient, Inst. Hautes Études Sci. Publ. Math. 76 (1992), 1–97. MR 1215592, DOI 10.1007/BF02699430
M. Masuda and T. Nagase, Equivariant algebraic vector bundles over adjoint representations, Osaka J. Math. 32 (1995), 701–708.
Mikiya Masuda and Ted Petrie, Equivariant algebraic vector bundles over representations of reductive groups: theory, Proc. Nat. Acad. Sci. U.S.A. 88 (1991), no. 20, 9061–9064. MR 1129884, DOI 10.1073/pnas.88.20.9061
Gerald W. Schwarz, Exotic algebraic group actions, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), no. 2, 89–94 (English, with French summary). MR 1004947