Representation of the algebra of linear maps by a skew product of algebras (Q2784530)
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scientific article; zbMATH DE number 1732424
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Representation of the algebra of linear maps by a skew product of algebras |
scientific article; zbMATH DE number 1732424 |
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Representation of the algebra of linear maps by a skew product of algebras (English)
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12 December 2002
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skew products
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algebras of linear operators
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local algebras
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An associative algebra \(S\) over a field \(k\) is a skew product of its subalgebras \(A,B\) if each element \(s\in S\) has a unique representation as a finite or an infinite sum \(s=a_0+a_1b_1+a_2b_2+\cdots\), where \(a_i\in A\) and \(b_1,b_2,\dots\) is a basis of \(B\). Let \(A\) be any algebra and \(B\) a generalized local algebra which is defined by some special properties. It is shown that the algebra of all linear operators on \(A\) is a skew product of \(A\) and \(B\).
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