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Associative 2-algebras and nonabelian extensions of associative algebras

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Abstract

In this paper, we study nonabelian extensions of associative algebras using associative 2-algebra homomorphisms. First we construct an associative 2-algebra using the bimultipliers of an associative algebra. Then we classify nonabelian extensions of associative algebras using associative 2-algebra homomorphisms. Finally we analyze the relation between nonabelian extensions of associative algebras and nonabelian extensions of the corresponding commutator Lie algebras.

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Acknowledgements

We give warmest thanks to the referee for helpful suggestions. This research is supported by NSFC (11922110).

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Authors and Affiliations

  1. Department of Mathematics, Jilin University, Changchun, 130012, Jilin, China

    Yunhe Sheng & You Wang

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  1. Yunhe Sheng
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  2. You Wang
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Correspondence to Yunhe Sheng.

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Communicated by James Stasheff.

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Sheng, Y., Wang, Y. Associative 2-algebras and nonabelian extensions of associative algebras. J. Homotopy Relat. Struct. 19, 63–77 (2024). https://doi.org/10.1007/s40062-024-00341-w

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