In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2. It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups. The most important class of graded quadratic algebras is Koszul algebras.
In mathematics, a quantum algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2.
( z1 algebra :ARG1-of ( z2 filter ) :ARG1-of ( z3 generate :ARG2 ( z4 element :mod ( z5 degree :ord ( z6 ordinal-entity :value 1 ) ) ) ) :ARG0-of ( z7 define :ARG1 ( z8 relate :ARG2 ( z9 degree :ord ( z10 ordinal-entity :value 2 ) ) ) ) :domain ( z11 algebra :mod ( z12 quantum ) ) :mod ( z13 mathematics ) )