References
- Dubois-Violette , M. , Kerner , R. ( 1997 ). Universal Z N -graded differential calculus . J. Geom. Phys. 23 ( 3–4 ): 235 – 246 .
- Dubois-Violette , M. , Kerner , R. ( 1996 ). Universal q-differential calculus and q-analog of homological algebra . Acta Math. Univ. Comenian. (N.S.) 65 ( 2 ): 175 – 188 .
- Dubois-Violette , M. ( 1996 ). Generalized differential spaces with d N = 0 and the q-differential calculus . Czechoslovak J. Phys. 46 ( 12 ): 1227 – 1233 , Quantum groups and integrable systems, I (Prague, 1996) .
- Dubois-Violette , M. ( 1998a ). d N = 0: generalized homology . K-Theory 14 ( 4 ): 371 – 404
- Dubois-Violette , M. ( 1998b ) . Generalized homologies for d N = 0 and graded q-differential algebras . Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math. , Vol 219 , Providence, RI : Amer. Math. Soc. , pp. 69 – 79 .
- Dubois-Violette , M. ( 2002 ) . Lectures on differentials, generalized differentials and on some examples related to theoretical physics . Quantum symmetries in theoretical physics and mathematics (Bariloche, 2000), Contemp. Math. , Vol. 294 , Providence, RI : Amer. Math. Soc. 2002 , pp. 59 – 94 .
- Edwin H. Spanier ( 1949 ). The Mayer homology theory . Bull. Amer. Math. Soc. 55 : 102 – 112 .
- Faddeev , L. D. , Reshetikhin , N. Yu , Takhtajan , L. A. ( 1988 ) . Quantization of Lie groups and Lie algebras . Algebraic analysis , Vol. I , Boston , MA : Academic Press , pp. 129 – 139 .
- Kapranov , M. M. On the q-analog of homological algebra arXiv:q-alg/9611005 .
- Kassel , C. ( 1995 ) . Quantum groups . New York : Springer-Verlag .
- Kassel , C. , Wambst , M. ( 1998 ). Algèbre homologique des N-complexes et homologie de Hochschild aux racines de l’unité . Publ. Res. Inst. Math. Sci. 34 ( 2 ): 91 – 114 .
- Kerner , R. , Abramov , V. (1999). On certain realizations of the q-deformed exterior differential calculus. Rep. Math. Phys. 43(1–2):179–194, Coherent states, differential and quantum geometry (Bia\l owieża, 1997).
- Manin , Yu. I. ( 1987 ). Some remarks on Koszul algebras and quantum groups . Ann. Inst. Fourier (Grenoble) 37 ( 4 ): 191 – 205 .
- Manin , Yu. I. ( 1988 ) . Quantum Groups and Noncommutative Geometry . Université de Montréal Centre de Recherches Mathématiques , Montreal , QC .
- Manin , Yu. I. ( 1992 ). Notes on quantum groups and quantum de Rham complexes . Teoret. Mat. Fiz. 92 ( 3 ): 425 – 450 .
- Mayer , W. ( 1942 ). A new homology theory, I, II . Ann. Math. 43 ( 2 ): 370 – 380 , 594–605 .
- Wess , J. , Zumino , B. ( 1990 ). Covariant differential calculus on the quantum hyperplane . Nuclear Phys. B Proc. Suppl. 18B : 302 – 312 (1991), Recent advances in field theory (Annecy-le-Vieux, 1990) .
- #Communicated by M. Cohen