Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T07:13:19.806Z Has data issue: false hasContentIssue false
  • English
  • Français

AUTOMORPHISMS OF QUANTUM MATRICES

Published online by Cambridge University Press:  01 October 2013

S. LAUNOIS  and
T. H. LENAGAN
S. LAUNOIS
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, United Kingdom e-mail: S.Launois@kent.ac.uk
T. H. LENAGAN
Affiliation:
Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, United Kingdom e-mail: tom@maths.ed.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the automorphism group of the algebra $\co_q(M_n)$ of n × n generic quantum matrices. We provide evidence for our conjecture that this group is generated by the transposition and the subgroup of those automorphisms acting on the canonical generators of $\co_q(M_n)$ by multiplication by scalars. Moreover, we prove this conjecture in the case when n = 3.

Keywords

20G4216W2016T2017B40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue A: New developments in Noncommutative Algebra and its applications. A conference in honour of Kenny Brown's and Toby Stafford's 60th birthdays. , October 2013 , pp. 89 - 100
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Alev, J. and Chamarie, M., Dérivations et automorphismes de quelques algèbres quantiques, Comm. Algebra 20 (1992), 1787–1802.Google Scholar
2.Kelly, A., Lenagan, T. H. and Rigal, L., Ring theoretic properties of quantum grassmannians, J. Algebra Appl. 3 (2004), 9–30.CrossRefGoogle Scholar
3.Launois, S. and Lenagan, T. H., Primitive ideals and automorphisms of quantum matrices, Algebr. Represent. Theor. 10 (4), 339–365.Google Scholar
4.Launois, S. and Lenagan, T. H., The first Hochschild cohomology group of quantum matrices and the quantum special linear group, J. Noncommut. Geom. 1 (2007), 281–309.Google Scholar
5.Parshall, B. and Wang, J.-P., Quantum linear groups, Mem. Amer. Math. Soc. 89 (439) (1991), vi–157.Google Scholar
6.Yakimov, M., The Launois–Lenagan conjecture, J. Algebra 392 (2013), 1–9.Google Scholar