quadratic algebra

A non-associative algebra A (with unity 1A) over a commutative ring R (with unity 1R) is called a quadratic algebra if A admits a quadratic formMathworldPlanetmath Q:AR such that

  1. 1.


  2. 2.

    the quadratic equation x2-b(1A,x)x+Q(x)1A=0 is satisfied by all xA, where b is the associated symmetric bilinear formMathworldPlanetmath given by b(x,y):=Q(x+y)-Q(x)-Q(y).

Title quadratic algebra
Canonical name QuadraticAlgebra
Date of creation 2013-03-22 15:11:38
Last modified on 2013-03-22 15:11:38
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 4
Author CWoo (3771)
Entry type Definition
Classification msc 17A45
Related topic QuadraticLieAlgebra