On associative and Lie 2-algebras (Q2837273)
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scientific article; zbMATH DE number 6186432
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On associative and Lie 2-algebras |
scientific article; zbMATH DE number 6186432 |
Statements
10 July 2013
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\(2\)-vector space
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Lie \(2\)-algebra
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associative \(2\)-algebra
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crossed module
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On associative and Lie 2-algebras (English)
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The class of Lie \(2\)-algebras is a categorification of the class of Lie algebras. It has a subclass consisting of strict Lie \(2\)-algebras, which is equivalent to the class of Lie crossed modules. This paper introduces classes of associative \(2\)-algebras and of strict associative \(2\)-algebras with analogous properties. The well-known adjunction between Lie algebras and associative algebras is extended to strict Lie \(2\)-algebras and strict associative \(2\)-algebras.
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