A cellular algebra with certain idempotent decomposition
نویسنده
چکیده
For a cellular algebra A with a cellular basis C, we consider a decomposition of the unit element 1A into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis C can be partitioned into some pieces with good properties. Then by using a certain map α, we give a coarse partition of C whose refinement is the original partition. We construct a Levi type subalgebra A α of A and its quotient algebra A α , and also construct a parabolic type subalgebra à α of A , which contains A α with respect to the map α. Then, we study the relation of standard modules, simple modules and decomposition numbers among these algebras. Finally, we study the relationship of blocks among these algebras.
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