Gr\"obner bases for *-algebars and faithful operator representations
  Sufficient conditions for existence of a faithful representation of a *-algebra in terms of its G\"obner basis is presented. Proposed construction of faithful representation is applicable to concrete examples: *-doubles, monomial *-algebras, extension of a *-algebras allowing Wick ordering and others. Several examples and counterexamples are presented. 
Stanislav Popovych, Kyrylo Vynogradov