Representation Spaces of the Jordan Plane

REFERENCES

• Antoniou , I. , Iyudu , N. , Wisbauer , R. ( 2003 ). On Serre's problem for RIT Algebra . Communications in Algebra 31 : 6037 – 6050 .
   Web of Science ®Google Scholar
• Antoniou , I. , Iyudu , N. ( 2001 ). Poincare–Hilbert series, PI and Noetherianity of the enveloping of the RIT Lie Algebra . Communications in Algebra 29 : 4183 – 4196 .
   Web of Science ®Google Scholar
• Antoniou , I. ( 1988 ). Internal Time and Irreversibility of Relativistic Dynamical Systems, Ph.D. dissertation, ULB, Brussels .
   Google Scholar
• Artin , M. , Schelter , W. F. ( 1987 ). Graded algebras of global dimension 3 . Adv. in Math. 66 : 171 – 216 .
   Web of Science ®Google Scholar
• Bergman , G. ( 1978 ). The diamond lemma for ring theory . Adv. in Math. 29 : 178 – 218 .
   Web of Science ®Google Scholar
• Cameron , P. , Iyudu , N. ( 2007 ). Graphs of relations and Hilbert series . Journal of Symbolic Computation 42 : 1066 – 1078 .
   Web of Science ®Google Scholar
• Crawley-Boevey , B. , Schröer , J. ( 2002 ). Irreducible components of varieties of modules . J. Reine Angew. Math. 553 : 201 – 220 .
   Web of Science ®Google Scholar
• Dixmier , J. ( 1968 ). Sur les algèbres de Weyl . Bull. Soc. Math. Fr. 96 : 209 – 242 .
   Google Scholar
• Dubrovin , B. A. , Fomenko , A. T. , Novikov , S. P. ( 1985 ). Modern Geometry—Methods and Applications. Part II. The Geometry and Topology of Manifolds . Graduate Texts in Mathematics , Vol. 104 . New York : Springer-Verlag , pp. 1 – 430 .
   Google Scholar
• Ershov , M. ( 2012 ). Golod-Shafarevich Groups: A Survey . pp. 1 – 51 . arxiv:1206.0490v1 .
   Google Scholar
• Etingof , P. , Ginzburg , V. ( 2007 ). Noncommutative Complete Intersections and Matrix Integrals . arXiv:math/0603272v3 .
   Google Scholar
• Etingof , P. ( 2009 ). Privat communication during the Newton institute activity on the algebraic lie theory .
   Google Scholar
• Gelfand , I. M. , Ponomarev , V. A. ( 1968 ). Indecomposable representations of the Lorenz Group . Russian Math. Surveys 23 : 1 – 58 .
   Google Scholar
• Gerstenhaber , M. ( 1961 ). On dominance and varieties of commuting matrices . Ann. of Math. 73 : 324 – 348 .
   Web of Science ®Google Scholar
• Golod , E. , Shafarevich , I. ( 1964 ). On the class field tower [Russian] . Izv. Akad. Nauk SSSR Ser. Mat. 28 : 261 – 272 .
   Google Scholar
• Green , Ed. ( 1994 ). An introduction to noncommutative Gröbner bases. In: Lecture Notes in Pure and Applied Mathematics 151:167–190 .
   Google Scholar
• Guralnick , R. (1992). A note on commuting pairs of matrices. Linear and Multilinear Algebra 31:71–75.
   Google Scholar
• Hazewinkel , M. , Gubareni , N. , Kirichenko , V. V. ( 2004 ). Algebras, Rings and Modules . Vol. 1. Mathematics and its Applications , Vol. 575 . Dordrecht : Kluwer Academic Publishers , pp. 1 – 380 .
   Google Scholar
• Iyudu , N. ( 2005 ). Classification of finite dimensional representations of one noncommutative quadratic algebra . Max-Planck-Institut für Mathematik Preprint Series 20 : 1 – 20 .
   Google Scholar
• Iyudu , N. , Wisbauer , R. ( 2009 ). Non-trivial stably free modules over crossed products . J. Phys. A 42 : 1 – 11 .
   Google Scholar
• Kontsevich , M. ( 2011 ). Noncommutative Identities . Mathematische Arbeitstagung, Max-Planck-Institut für Mathematik , pp. 1 – 9 .
   Google Scholar
• Kontsevich , M. , Belov-Kanel , A. ( 2005 ). Automorphisms of the Weyl algebra . Lett. Math. Phys. 74 : 181 – 199 .
   Web of Science ®Google Scholar
• Korenskii , S. ( 1991 ). Representations of the Quantum group SL J (2) . Rus. Math. Surv. 46 : 211 – 212 .
   Web of Science ®Google Scholar
• Makar-Limanov , L. ( 1984 ). On automorphisms of Weyl algebra . Bull. Soc. Math. France 112 : 359 – 363 .
   Web of Science ®Google Scholar
• Manin , Yu. I. Quantum Groups and Noncommutative Geometry . CRM .
   Google Scholar
• Motzkin , T. , Taussky-Todd , O. ( 1955 ). Pairs of matrices with property L. II . Trans. AMS 80 : 387 – 401 .
   Google Scholar
• Mumford , D. ( 1999 ). Red Book of Varieties and Schemes , LNM 1358 , Springer .
   Google Scholar
• Odesskii , A. ( 1989 ). Sklyanin's elliptic algebras . Func. Anal. Appl. 23 : 207 – 214 .
   Web of Science ®Google Scholar
• Priddy , S. ( 1970 ). Koszul resolutions . Trans. Amer. Math. Soc. 152 : 39 – 60 .
   Google Scholar
• Ringel , C. M. The Representation Type of Local Algebras . LNM 488. Springer .
   Google Scholar
• Schröer , J. ( 2004 ). Varieties of pairs of nilpotent matrices annihilating each other . Comment. Math. Helv. 79 : 396 – 426 .
   Web of Science ®Google Scholar
• Smoktunowicz , A. ( 2012 ). Golod-Shafarevich Algebras, Free Subalgebras and Noetherian Images . arxiv1207.6503 .
   Google Scholar
• Smoktunowicz , A. ( 2009 ). Growth of modules over generic Golod-Shafarevich algebras . Asian-European J. Math. 2 : 279 – 283 .
   Google Scholar
• Bartholdi , L. , Smoktunowicz , A. ( 2011 ). Images of Golod-Shafarevich Algebras with Small Growth . arxiv1108.4264 .
   Google Scholar
• Stafford , J. T. , van den Bergh , M. ( 2001 ). Noncommutative curves and noncommutative surfaces . Bull. Amer. Math. Soc. (N. S.) 38 : 171 – 216 .
   Web of Science ®Google Scholar
• Voden , T. ( 2009 ). Subalgebras of Golod-Shafarevich algebras . Int. J. Algebra Comput. 423 ( 19 ).
   Google Scholar
• Wadsworth , A. ( 1990 ). The algebra generated by two commuting matrices . Linear and Multilinear Algebra 27 : 159 – 162 .
   Google Scholar
• Zelmanov , E. ( 2007 ). Some open problems in the theory of infinite dimensional algebras . J. Korean Math. Soc. 44 : 1185 – 1195 .
   Web of Science ®Google Scholar
• Communicated by A. Smoktunowicz.
   Google Scholar