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Abstract
We investigate group gradings of upper block triangular matrix algebras over a field such that all the matrix units lying there are homogeneous elements. We describe these gradings as endomorphism algebras of graded flags and classify them as orbits of a certain biaction of a Young subgroup and the group G on the set G n , where G is the grading group and n is the size of the matrix algebra. In particular, the results apply to algebras of upper triangular matrices.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
This work was supported by the UEFISCDI grant PN-II-ID-PCE-2011-3-0635, contract no. 253/5.10.2011. The first author was also supported by the Sectorial Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and by the Romanian Government under the contract number SOP HRD/107/1.5/S/82514.
Notes
Communicated by J. L. Gomez Pardo.