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Enveloping Algebras of Certain Types of Color Hom-Lie Algebras

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Book cover Algebraic Structures and Applications (SPAS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 317))

Abstract

In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free hom-associative color algebra on a hom-module is described for a certain type of color hom-Lie algebras and is applied to obtain the universal enveloping algebra of those hom-Lie color algebras. Finally, this construction is applied to obtain the extension of the well-known Poincaré–Birkhoff–Witt theorem for Lie algebras to the enveloping algebra of the certain types of color hom-Lie algebra such that some power of the twisting map is the identity map.

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Acknowledgements

Abdoreza Armakan is grateful to the research environment in Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics at the School of Education, Culture and Communication at Mälardalen University, Västerås, Sweden for providing support and excellent research environment during his visits to Mälardalen University when part of the work on this paper has been performed.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran

    Abdoreza Armakan

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Box 883, 72123, Västerås, Sweden

    Sergei Silvestrov

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  1. Abdoreza Armakan
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  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  3. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Armakan, A., Silvestrov, S. (2020). Enveloping Algebras of Certain Types of Color Hom-Lie Algebras. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_10

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