Polynomial group laws. II
HTML articles powered by AMS MathViewer
- by Zensho Nakao
- Proc. Amer. Math. Soc. 80 (1980), 196-200
- DOI: https://doi.org/10.1090/S0002-9939-1980-0577743-X
- PDF | Request permission
Abstract:
Let V be a Zariski-open (i.e., cofinite) subset of an infinite field K. Call a map $m:V \times V \to V$ separately polynomial if for each $x \in V$ the two partial maps $y \to m(x,y),y \to m(y,x)$ are polynomial. If $m:V \times V \to V$ is a separately polynomial group law, then either $V = K$ and $m(x,y) = x + y + k$ for some $k \in K$ or $V = K - \{ k\}$ and $m(x,y) = b(x - k)(y - k) + k$ for some $k \in K$ and $b \in {K^\ast } = K - \{ 0\}$.References
- Andy R. Magid, Separately algebraic group laws, Amer. J. Math. 100 (1978), no. 2, 407–409. MR 489964, DOI 10.2307/2373855
- Zensho Nakao, Bi-algebraic groups, J. Algebra 57 (1979), no. 1, 1–9. MR 533097, DOI 10.1016/0021-8693(79)90205-9
- Zensho Nakao, Polynomial group laws, Amer. Math. Monthly 87 (1980), no. 9, 735–736. MR 602832, DOI 10.2307/2321864
- Richard S. Palais, Some analogues of Hartogs’ theorem in an algebraic setting, Amer. J. Math. 100 (1978), no. 2, 387–405. MR 480509, DOI 10.2307/2373854
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 196-200
- MSC: Primary 14L17; Secondary 20G15
- DOI: https://doi.org/10.1090/S0002-9939-1980-0577743-X
- MathSciNet review: 577743