Abstract
We determine the number of isomorphism classes of elementary gradings by a finite group on an algebra of upper block-triangular matrices. As a consequence we prove that, for a finite abelian group G, the sequence of the numbers E(G,m) of isomorphism classes of elementary G-gradings on the algebra Mm(F) of m×m matrices with entries in a field F characterizes G. A formula for the number of isomorphism classes of gradings by a finite abelian group on an algebra of upper block-triangular matrices over an algebraically closed field, with mild restrictions on its characteristic, is also provided. Finally, if G is a finite abelian group, F is an algebraically closed field and N(G,m) is the number of isomorphism classes of G-gradings on Mm(F) we prove that N(G,m)∼1|G|!m|G|−1∼E(G,m).
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.
