Geodesic
Representations of $*$-algebras with two generators and polynomial relations
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 10, Tome 172 (1989), pp. 121-129

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It is proved that all $*$-algebras with quadratic relations are tame; a classification of their representations is given. Examples of algebras with general polynomial relations (both tame and wild) are studied. 
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     author = {V. L. Ostrovsky and Yu. S. Samoilenko},
     title = {Representations of $*$-algebras with two generators and polynomial relations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--129},
     publisher = {mathdoc},
     volume = {172},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a10/}
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V. L. Ostrovsky; Yu. S. Samoilenko. Representations of $*$-algebras with two generators and polynomial relations. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 10, Tome 172 (1989), pp. 121-129. http://geodesic.mathdoc.fr/item/ZNSL_1989_172_a10/