Abstract
Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Note aims to demonstrate that Manin's construction can be extended for quantum spaces which are non-quadratic homogeneous algebras. The Artin–Schelter classification of regular algebras of global dimension three contains two types of algebra: quadratic and cubic. Ewen and Ogievetsky classified the quantum matrix groups which are deformations of GL(3) corresponding to the quadratic algebras in the Artin–Schelter classification. In this Note we consider the cubic Artin–Schelter algebras as quantum spaces and construct Hopf algebras of their automorphisms. To cite this article: T. Popov, C. R. Acad. Sci. Paris, Ser. I 338 (2004).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
