\(\ell\)-hereditary triangular matrix algebras of tame type (Q1121360)
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scientific article; zbMATH DE number 4103297
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\ell\)-hereditary triangular matrix algebras of tame type |
scientific article; zbMATH DE number 4103297 |
Statements
\(\ell\)-hereditary triangular matrix algebras of tame type (English)
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1990
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We call \(T_ 2(A)=\left[ \begin{matrix} A\\ 0\end{matrix} \begin{matrix} A\\ A\end{matrix} \right]\) a triangular matrix algebra over an algebra A. Recall that an algebra A is called \(\ell\)-hereditary if any left (right) ideal in A with a unique maximal left (right) submodule is projective. The main result is the description of \(\ell\)-hereditary algebras A such that the algebras \(T_ 2(A)\) are of tame type. This characterization is obtained in terms of the Gabriel quiver of the algebra A.
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triangular matrix algebra
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\(\ell \)-hereditary algebras
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tame type
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Gabriel quiver
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0.8253825902938843
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0.8188208937644958
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0.816692590713501
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0.815238356590271
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