Quantizations of braided derivations. 2. Graded modules
Lobachevskii journal of mathematics, Tome 25 (2007), pp. 131-160.

Voir la notice de l'article provenant de la source Math-Net.Ru

For the monoidal category of graded modules we find braidings and quantizations. We use them to find quantizations of braided symmetric algebras and modules, braided derivations, braided connections, curvatures and differential operators.
@article{LJM_2007_25_a2,
     author = {H. L. Huru},
     title = {Quantizations of braided derivations. 2. {Graded} modules},
     journal = {Lobachevskii journal of mathematics},
     pages = {131--160},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_25_a2/}
}
TY  - JOUR
AU  - H. L. Huru
TI  - Quantizations of braided derivations. 2. Graded modules
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 131
EP  - 160
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_25_a2/
LA  - en
ID  - LJM_2007_25_a2
ER  - 
%0 Journal Article
%A H. L. Huru
%T Quantizations of braided derivations. 2. Graded modules
%J Lobachevskii journal of mathematics
%D 2007
%P 131-160
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_25_a2/
%G en
%F LJM_2007_25_a2
H. L. Huru. Quantizations of braided derivations. 2. Graded modules. Lobachevskii journal of mathematics, Tome 25 (2007), pp. 131-160. http://geodesic.mathdoc.fr/item/LJM_2007_25_a2/

[1] Henri Cartan, Samuel Eilenberg, Homological algebra, Princeton University Press, 1956 | MR | Zbl

[2] V. Chari, A. Pressley, A Guide to Quantum Groups, Cambridge University Press, 1994 | MR | Zbl

[3] S. Eilenberg, S. Mac Lane, “Cohomology Theory in Abstract Groups 1”, Annals of Mathematics, 48:1 (1947), 51–78 | DOI | MR | Zbl

[4] C. Faith, Algebra: Rings, Modules and Categories. I, Die Grundlehren der mathemathischen Wissenschaften in Einzeldarstellungen, 190, Springer-Verlag, 1973 | MR | Zbl

[5] D. Gurevich, “The Yang Baxter equation and generalizations of formal Lie theory”, Soviet Math. Dokl., 33 (1986), 758–762 | MR | Zbl

[6] D. Gurevich, “Algebraic aspects of quantum Yang-Baxter equation”, Algebra i Analiz, 2:4 (1990), 119–148 | MR | Zbl

[7] D. Gurevich, A. Radul, V. Rubtsov, “Non-commutative differential geometry and Yang–Baxter equation”, Intitute des Hautes Etudies Scientifiques, 88 (1991)

[8] H. L. Huru, “Associativity constraints, braidings and quantizations of modules with grading and action”, Lobachevskii Journal of Mathematics, 23 (2006), 5–27 | MR | Zbl

[9] H. L. Huru, “Quantization of braided algebras. 1. Monoidal categories”, Lobachevskii Journal of Mathematics, 24 (2006), 13–24 | MR | Zbl

[10] H. L. Huru, “Quantization of braided algebras. 3. Modules with action by a group”, Lobachevskii Journal of Mathematics, 24 (2006), 161–185 | MR

[11] H. L. Huru, Braided symmetric and exterior algebras and quantizations of braided Lie algebras

[12] H. L. Huru, V. V. Lychagin, Quantization and classical non-commutative and non-associative algebras, preprint, Institut Mittag-Leffler, Stockholm, 2005 | MR | Zbl

[13] P. K. Jakobsen, V. Lychagin, The Categorical Theory of Relations and Quantizations, 2001

[14] Cathrine V. Jensen, Linear ordinary differential equations and $D$-modules, solving and reduction methods, Dr.Scient. thesis, The University of Tromsø, Nov. 2004

[15] V. V. Lychagin, Quantizations of Braided Differential Operators, Erwin Schrödinger International Institute of Mathematical Physics, Wien, and Sophus Lie Center, Moscow, 1991

[16] V. V. Lychagin, Differential operators and quantizations, Preprint series in Pure Mathematics, Matematisk institutt, Universitetet i Oslo, No. 44, 1993

[17] V. V. Lychagin, “Calculus and Quantizations Over Hopf Algebras”, Acta Applicandae Mathematicae, 1–50

[18] V. V. Lychagin, “Quantizations of Differential Equations”, Pergamon Nonlinear Analysis, 47 (2001), 2621–2632 | DOI | MR | Zbl

[19] Saunders Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics, 5, Springer, 1998 | MR | Zbl