Faithful representations of association schemes

Faithful Linear Representations of Bands

A band is a semigroup consisting of idempotents. It is proved that for any field K and any band S with finitely many components, the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative K-algebra. The proof of a theorem of Malcev [4, Theorem 10] on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if S = F ∪ E is a b...

Faithful Representations of Polishable Ideals

faithful real representations of cyclically pinched one-relator groups

‎‎in cite{fr 1‎, ‎fr 2} using faithful complex representations of cyclically pinched and conjugacy pinched one-relator groups we proved that any limit group has a faithful representation in $psl(2,c)$‎. ‎further this representation can be effectively constructed using the jsj decomposition‎. ‎in this note we show that any hyperbolic cyclically pinched one-relator group with maximal amalgamated ...

On Faithful Representations of Lie Groups

where tE:R and I is the unit matrix of degree d. Let GL(K, d) denote the group of all nonsingular matrices of degree d with coefficients in K. Any subgroup of GL(K, d) will be called a linear group of degree d. Let 0 be the identity representation of a linear Lie group G with the Lie algebra 8 so that 9(x) =x (*EG). Then dd is a faithful representation of g and exp dd(X) =0(exp X) =exp X for an...

On minimal degrees of faithful quasi-permutation representations of nilpotent groups

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....