Termination for a class of algorithms for constructing algebras given by generators and relations
The article presents a class of algorithms which allows to create a multiplication table for a finitely-presented nonassociative (known to be finite-dimensional) algebra. The main example is a Lie algebra. The idea is to work in the free nonassociative algebra (instead of a free Lie algebra, for example) and to rewrite partial multiplication tables, using identities. The main assumption is that it is sufficient to verify identities on a linear basis. Under some assumptions the termination of the algorithms is guaranteed.
scientific article; zbMATH DE number 1025706