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7.7.13.0. findimAlgebra
Procedure from library nctools.lib (see nctools_lib).
- Usage:
- findimAlgebra(M,[r]); M a matrix, r an optional ring
- Return:
- ring
- Purpose:
- define a finite dimensional algebra structure on a ring
- Note:
- the matrix M is used to define the relations x(i)*x(j) = M[i,j] in the
basering (by default) or in the optional ring r.
The procedure equips the ring with the noncommutative structure.
The procedure exports the ideal (not a two-sided Groebner basis!), called fdQuot , for further qring definition.
- Theory:
- finite dimensional algebra can be represented as a factor algebra
of a G-algebra modulo certain two-sided ideal. The relations of a f.d. algebra are thus naturally divided into two groups: firstly, the relations
on the variables of the ring, making it into G-algebra and the rest of them, which constitute the ideal which will be factored out.
Example:
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