𝑆𝐾₁ of 𝑛 lines in the plane

Roberts, Leslie G.

doi:10.1090/S0002-9947-1976-0422278-1

$SK\sb{1}$ of lines in the plane

Author: Leslie G. Roberts
Journal: Trans. Amer. Math. Soc. 222 (1976), 353-365
MSC: Primary 14F15; Secondary 14C20
DOI: https://doi.org/10.1090/S0002-9947-1976-0422278-1
MathSciNet review: 0422278
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We calculate $S{K_1}(A)$ where A is the coordinate ring of the reduced affine variety consisting of n straight lines in the plane.

[1] S. Antoy, Sul calcolo del gruppo di Picard di certe estensioni intere semplici, Ann. Univ. Ferrara Sez. VII 18 (1973), 155-167. MR 48 #11083. MR 0332757 (48:11083)
[2] R. K. Dennis and M. Krusemeyer, ${K_2}$ of , a problem of Swan, and related computations (to appear).
[3] R. K. Dennis and M. R. Stein, The functor ${K_2}$ , a survey of computations and problems, Lecture Notes in Math., vol. 342, Springer-Verlag, Berlin and New York, 1973, pp. 243-280. MR 0354815 (50:7292)
[4] J. Graham, Continuous symbols on fields of formal power series, Lecture Notes in Math., vol. 342, Springer-Verlag, Berlin and New York, 1973, pp. 474-486. MR 0364187 (51:442)
[5] J. Labute and P. Russell, On ${K_2}$ of truncated polynomial rings, J. Pure Appl. Algebra 6 (1975), 239-251. MR 0396595 (53:457)
[6] J. Milnor, Introduction to algebraic K-theory, Princeton Univ. Press, Princeton, N.J. 1971. MR 0349811 (50:2304)
[7] F. Orecchia, Sui gruppi di Picard di certe algebre finite non integre, Ann. Accad. Sci. Torino (to appear). MR 0404258 (53:8061)
[8] L. G. Roberts, Higher derivations and the Jordan canonical form of the companion matrix, Canad. Math. Bull. 15 (1972), 143-144. MR 47 #5021. MR 0316474 (47:5021)
[9] -, The K-theory of some reducible affine varieties, J. Algebra 35 (1975), 516-527. MR 0404259 (53:8062)
[10] W. van der Kallen, H. Maazen and J. Stienstra, A presentation for some ${K_2}(n,R)$ , Bull. Amer. Math. Soc. 81 (1975), 934-936. MR 0376818 (51:12993)