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Quasigroup homogeneous spaces and linear representations. (English) Zbl 0994.20054

The aim of the present paper is to describe the structure of the ring \((\pi(\mathbb{C} G),+,E_P)\) and its representation \[ \rho_{P\setminus Q}\colon(\pi(\mathbb{C} G),+,E_P)\to\text{End}_\mathbb{C}\mathbb{C} P\setminus Q.\tag{1} \] In the final section the author examines sufficient conditions for commutativity of the image of (1), implying mutual commutativity of the various transition matrices \(R_{P\setminus Q}(q)=A^+_PR(q)A_P\) in the corresponding iterated function system.

MSC:

20N05 Loops, quasigroups
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