Cellular algebras and Frobenius extensions arising from two-parameter permutation matrices
DOI:
https://doi.org/10.3842/umzh.v76i12.7976Keywords:
Invariant subring; σ-φ permutation matrix; Cellular algebraAbstract
UDC 512.5
Let n be a positive integer, let R be a (unitary associative) ring, and let Mn(R) be the ring of all n by n matrices over R. For a permutation σ in the symmetry group Σn and a ring automorphism φ of R, we introduce the definition of σ-φ permutation matrices. The set Bn(σ,φ,R) of all σ-φ permutation matrices is proved to be a subring of Mn(R). We show that the extension Bn(σ,φ,R)⊆Mn(R) is a separable Frobenius extension. Moreover, if R is a commutative cellular algebra over the invariant subring Rφ of R, then Bn(σ,φ,R) is also a cellular algebra over Rφ.
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