Search

Abstract: In this paper we will study the structure of algebras associated to two directed, layered graphs Γ. These are algebras associated with Hasse graphs of n-gons and the algebras related to pseudoroots of noncommutative polynomials. We will find the filtration preserving automorphism group of these algebras and then we will find the multiplicities of the irreducible representations of acting on the homogeneous components of and . [Copyright &y& Elsevier]

In this paper we split the defining relations of the two well known one-parameter quantizations of GL(2), Manin and Dipper–Donkin, into two bialgebras. We recombine these bialgebras to obtain two-parameter quantum groups. We find “one-sided preantipodes” for these bialgebras. By fixing the condition for these maps to be an antiautomorphism of the whole algebra and setting particular commuting relations for the corresponding determinant, we recover the Manin and Dipper–Donkin quantization plus an additional quantum group that is a particular case of the two-parameter Takeuchi quantum group. [Copyright &y& Elsevier]