Sunto
Vengono classificate le azioni delle algebre di Hopf puntate di dimensione finita sul toro quantico generico.
Abstract
Actions of finite dimensional pointed Hopf algebras on generic quantum torus are classified.
References
[AC]J. Alev—M. Chamarie,Dérivations et automorphismes de quelques algèbres quantiques, Comm. Algebra20 (1992), 1787–1802.
[Andr1]Nicolas Andruskiewitsch,About finite dimensional Hopf algebras. Contemporary Mathematics294 (2002), 1–57.
[Andr2]Nicolas Andruskiewitsch—H.-J. Schneider,On the coradical filtration of Hopf algebras whose coradical is a Hopf subalgebra. Bol. Acad. Nacional de Ciencias (Cordoba)65 (2000), pp. 45–51.
[Andr3]Nicolas Andruskiewitsch—H.-J. Schneider,Pointed Hopf algebras. In «New directions in Hopf algebras», MSRI series (Cambridge Univ. Press; 2002) 1–68.
[Art1]V. A. Artamonov,Automorphisms of division rings of quantum rational fucntions, Mat. Sbornik,191 (2000), N 12, 3–26.
[Art2]V. A. Artamonov,Pointed Hopf algebras acting on quantum polynomials, J. Algebra259 (2003), N 2, 323–352.
[Art3]V. A. Artamonov,Actions of quantum groups of quantum spaces. Vestnik Moscow University, ser. mat. mech.,3 (2003), 13–17.
[Art4]V. A. Artamonov,Generalized derivations of a quantum plane. J. Math. Sci. (to appear)
[AW]V.A. Artamonov—R. Wisbauer,Homological properties of quantum polynomials, Algebras and representation theory,4 (2001), N 3, 219–247.
[BrG]K. A. Brown—K. R. Goodearl,Lecture on algebraic quantum groups. Birkhäuser, Basel, (Boston, 2002).
[J] N. Jacobsom,Structure of rings, Amer. Math. Soc., Colloq. Publ., v. 37, AMS, 1968.
[M]S. Montgomery,Hopf Algebras and Their Actions on Rings, Regional Conf. Ser. Math. Amer. Math. Soc., Providence RI, 1993.
[MP]J.C. McConnell—J.J. Pettit,Crossed products and multiplicative analogues of Weyl algebras. J. London Math. Soc.38 (1988), N 1., P. 47–55.
[OP]J. P. Osborn—D. Passman,Derivations of skew polynomial rings. J. Algebra,176 (1995), N 2, 417–448.
[R]L. Richard,Surles endomorphismes des tores quantiques. Commun. Algebra.30 (2002) N 11.—c. 5282–5306.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research partially supported by grants RFBR 03-01-00167, NSh-1910.2003.1 and INTAS00-566
Rights and permissions
About this article
Cite this article
Artamonov, V.A. Actions of Pointed Hopf Algebras on Quantum Torus. Ann. Univ. Ferrara 51, 29–60 (2005). https://doi.org/10.1007/BF02824822
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02824822