On representation of the \(*\)-algebra \(P_{N,1+\frac{1}{N-1}}\) (Q2754851)
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scientific article; zbMATH DE number 1668469
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On representation of the \(*\)-algebra \(P_{N,1+\frac{1}{N-1}}\) |
scientific article; zbMATH DE number 1668469 |
Statements
4 November 2001
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\(*\)-algebra
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orthoprojection
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quiver
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complex *-algebra
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irreducible representation
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0.8883755
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0.88653606
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0.88067824
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0.87772053
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0.8737418
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On representation of the \(*\)-algebra \(P_{N,1+\frac{1}{N-1}}\) (English)
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The authors consider a complex \(*\)-algebra with the unit \(e\), generators \(p_1,\ldots ,p_n\), and relations NEWLINE\[NEWLINE p_i=p_i^2=p_i^*\;(i=i,\ldots ,n),\quad \sum_{i=1}^np_i=\left( 1+\frac{1}{N-1}\right) e. NEWLINE\]NEWLINE The authors use the theory of \(*\)-quivers to prove the existence and uniqueness, up to unitary equivalence, of a \((n-1)\)-dimensional irreducible representation. Another proof was found recently by \textit{V. I. Rabanovich} and \textit{Yu. S. Samoilenko} (submitted to Ukr. Mat. Zh.). An explicit form of this representation is found.
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