Degree-inverting involutions on matrix algebras

Abstract

Let F be an algebraically closed field of characteristic zero, and G be a finite abelian group. If is a G-graded algebra, we study degree-inverting involutions on A, i.e. involutions on A satisfying , for all . We describe such involutions for the full matrix algebra over F and for the algebra of upper triangular matrices.

Keywords:

• Matrix algebras
• involutions
• graded algebras
• upper-triangular matrices

AMS Subject Classifications:

• 16W50
• 16S50
• 16W10

Acknowledgements

This work was started when the authors were visiting IMPA in (Brazilian) summer 2016. The authors would like to thank IMPA for the hospitality and for the financial support. The authors would like to thank the Referee for his/her valuable comments that improved the presentation of the paper. T.C. de Mello would like to thank F. Martino for useful comments on .

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Fapesp [grant number 2014/10352-4], [grant number 2014/09310-5], and CNPq [grant number 461820/2014-5].