A special case of filtered algebra is a graded algebra. In general there is the following construction that produces a graded algebra out of a filtered algebra.
Let be a filtered algebra then the associated http://planetmath.org/node/3071graded algebra is defined as follows:
As a vector space
the multiplication is defined by
The multiplication is well defined and endows with the of a graded algebra, with gradation . Furthermore if is associative then so is .
The underlying vector spaces of and are isomorphic.
|Date of creation||2013-03-22 13:23:55|
|Last modified on||2013-03-22 13:23:55|
|Last modified by||Dr_Absentius (537)|