Free Algebra Ontology

An informal description of the Ontology of the Free Algebra Knowledge Base developed so far.

Metadata and Semantics

All Free Algebra instances belong to the owl:Class sd:FreeAlgebra with predicates

• sd:hasVariables Literal - comma separated list of (non commuting) variables
• sd:hasParameters Literal - comma separated list of (commuting) parameters
• sd:uptoDegree Literal - integer, semantics to be fixed
• sd:relatedXMLResource URI - the Resource file
• standard predicates sd:createdAt, sd:createdBy, rdfs:comment

The free algebra is the factor of the non commutative polynomial ring Q(a1,…,ak)<x1,…,xn> over the commtative field Q(a1,…,ak) of rational functions in a1,…,ak by the twosided ideal generated by the given non commutative polynomials.

XML-Resources

The XML-Resource contains mainly the following tags

• - a list x1,...,xn of (non commuting) variables,
• (optionally) - a list a1,...,ak of (commuting) parameters
• (optionally) - an integer (meaning has to be specified)
• - a sequence of entries of non commutative polynomials

For details see the XSchema description FreeAlgebras.xsd.