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7.4.1 G-algebras
Definition (PBW basis)
Definition (G-algebra)
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- non-degeneracy conditions:
Note: Note that non-degeneracy conditions simply ensure associativity of multiplication.
Theorem (properties of G-algebras)
Setting up a G-algebra
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- define a commutative ring
equipped with a monomial ordering
(see ring declarations (plural)).
This provides us with the information on a field
(together with its parameters), variables
and an ordering <.
From the sequence of variables we will build a G-algebra with the Poincaré-Birkhoff-Witt (PBW) basis
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- define strictly
upper triangular matrices (of type
matrix )
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Call the initialization function
nc_algebra(C,D) (see nc_algebra) with the data
At present, PLURAL does not check automatically whether the non-degeneracy conditions
hold but it provides a procedure ndcond from the library nctools_lib to check this.
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