Dokovic, D. Z., and Lowell G. Sweet. “Infinite Homogeneous Algebras Are Anticommutative”. Proceedings of the American Mathematical Society, vol. 127, no. 11, 1999, pp. 3169-74, https://scholar2.islandarchives.ca/islandora/object/ir%3Air-batch6-1692.

Genre

  • Journal Article
Contributors
Author: Dokovic, D. Z.
Author: Sweet, Lowell G.
Date Issued
1999
Abstract

A (non-associative) algebra A, over a field k, is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces of A. Suppose A is a nontrivial finite dimensional homogeneous algebra over an infinite field. Then we prove that x(2) = 0 for all x in A, and so xy = yx for all x; y is an element of A.

Note

Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada. Univ Prince Edward Isl, Dept Math, Charlottetown, PE C1A 4P3, Canada.; Dokovic, DZ, Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada.

PROVIDENCE; 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA

AMER MATHEMATICAL SOC

PT: J; CR: ARTAMONOV VA, 1977, MATH USSR SB, V33, P375 BOEN J, 1962, PAC J MATH, V12, P817 DJOKOVIC DZ, 1973, P AM MATH SOC, V41, P457 GROSS F, 1971, P AM MATH SOC, V4, P10 IVANOV DN, 1982, VESTNIK MOSKOV U MAT, V37, P69 KOSTRIKIN AI, 1965, IZVESTIYA AKAD NAUK, V29, P471 MACDOUGALL JA, 1978, PAC J MATH, V74, P153 SHULT EE, 1969, ILLINOIS J MATH, V13, P654 SWEET LG, 1975, P AM MATH SOC, V48, P321 SWEET LG, 1975, PAC J MATH, V59, P585 SWEET LG, 1987, PAC J MATH, V129, P375; NR: 11; TC: 1; J9: PROC AMER MATH SOC; PG: 6; GA: 225KL

Source type: Electronic(1)

Language

  • English

Subjects

  • hypersurface
  • non-associative algebras
  • Mathematics, Applied
  • Mathematics
  • automorphism group
Page range
3169-3174
Host Title
Proceedings of the American Mathematical Society
Host Abbreviated Title
Proc.Amer.Math.Soc.
Volume
127
Issue
11
ISSN
0002-9939

Department