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- W3049174306 abstract "Abstract An infinite dimensional associative algebra <?CDATA ${mathcal{A}}$?> <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> over a field <?CDATA ${mathbb{F}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=double-struck>F</mml:mi> </mml:math> is called locally finite associative algebra if every finite set of elements is contained in a finite dimensional subalgebra of <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> . Given any associative algebra <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> over field <?CDATA ${mathbb{F}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=double-struck>F</mml:mi> </mml:math> of any characteristic. Consider a new multiplication on <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> called the Lie multiplication which defined by [ a, b ] = ab − ba for all a, b ∈ A , where ab is the associative multiplication in <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> . Then L = <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> (−) together with the Lie multiplication form a Lie subalgebra of <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> . It is natural to expect that the structures of L and <?CDATA ${mathcal{A}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=script>A</mml:mi> </mml:math> are connected closely. In this paper, we study and discuss the structure of infinite dimensional locally finite Lie and associative algebras. The relation between them, their ideals and their inner ideals is considered. A brief discussion of the simple associative algebras and simple Lie algebras is also be provided." @default.
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- W3049174306 date "2020-07-01" @default.
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- W3049174306 title "Locally Finite Associative Algebras and Their Lie Subalgebras" @default.
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- W3049174306 doi "https://doi.org/10.1088/1742-6596/1591/1/012058" @default.
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