Quasigroup homogeneous spaces and linear representations (Q5946415)
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scientific article; zbMATH DE number 1658813
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasigroup homogeneous spaces and linear representations |
scientific article; zbMATH DE number 1658813 |
Statements
Quasigroup homogeneous spaces and linear representations (English)
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27 February 2002
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quasigroups
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linear representations
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group rings
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Latin squares
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permutation actions
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commutativity
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transition matrices
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iterated function systems
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0.9187833
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0.91434467
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0.91129196
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0.90609056
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The aim of the present paper is to describe the structure of the ring \((\pi(\mathbb{C} G),+,E_P)\) and its representation NEWLINE\[NEWLINE\rho_{P\setminus Q}\colon(\pi(\mathbb{C} G),+,E_P)\to\text{End}_\mathbb{C}\mathbb{C} P\setminus Q.\tag{1}NEWLINE\]NEWLINE 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.
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